The Hog offensive unit averaged 5.0 yards per play, and 357 yards per game, the seventh-best mark in 1962. Arkansas also averaged 28.6 points per game, the fifth highest average nationally. Running on the Razorback defense was tough, as the unit gave up 90.7 yards per contest, the seventh-lowest total in the nation.
The 1963 Sugar Bowl matched up rivals Arkansas and Ole Miss in the Razorbacks second straight Sugar Bowl, and fourth bowl in four seasons. The Rebels also had reached four consecutive bowl games.
After each team kicked field goals, Ole Miss scored the first touchdown, a 33-yard strike from Glynn Griffing to Louis Guy that gave the Rebels a 10–3 lead. The Hogs replied with a five-yard touchdown toss from Billy Moore to knot the game at 10. Ole Miss QB Griffing then scored on a one-yard touchdown scamper. The Razorbacks would tack on a field goal, but, as neither team could dent the scoreboard in the fourth quarter, would lose by a 17–13 final.
Razorback Guard Ronnie Caveness was named an All-American. Ken Hatfield again led the nation in punt return yards, with 518. Tom McKnelly scored 45 points, kicking 27 extra points and 6 field goals, tying him with LSU's Doug Moreau for fourth place nationally.
Arkansas' total defense was fourth-best, allowing only 180.5 yards per game, while the scoring defense was the best in the land, giving up only 5.7 points per game.
Arkansas and Nebraska met for the first time in the 1965 Cotton Bowl Classic in Dallas, Texas. Arkansas' number-one rated defense was giving up only 5.7 points per game, where Nebraska's #7 scoring offense was scoring 24.9 points per contest.
A standing-room-only crowd watched as the Hogs opened the scoring on a Tom McKnelly field goal, but the Huskers responded with Harry Wilson punching it in from one yard out. The third quarter passed with no scoring before Bobby Burnett of Arkansas ran in for the go-ahead touchdown. Despite being named the AP Poll and Coaches' Poll national champion, #1 Alabama could not hold off Texas in the Orange Bowl, which left Arkansas to take the number-one spot in the FWAA Poll and a share of that year's national championship.
Arkansas was invited to play in the Cotton Bowl Classic on January 1, 1965 against the Nebraska Cornhuskers. The Razorbacks went on to beat the Cornhuskers 10–7 and were selected as national champions by the Football Writers Association of America and the Helms Athletic Foundation as the #1 Alabama Crimson Tide lost their bowl game against the Texas Longhorns, a team Arkansas had beaten in Austin. Because the final AP and Coaches (UPI) Polls were released before bowl games were played at the time, the Crimson Tide was selected national champions by the AP and Coaches' (UPI) Polls. Because of the controversy, the AP Poll experimented with a voting model that took the final vote to select their champion after the bowl games in the 1965 season. In 1966, the AP Poll went back to taking the final vote at the conclusion of the regular season before finally adopting the post- bowl season model in 1968. The Coaches' Poll adopted the post-bowl season model in 1974 after the controversies surrounding the 1964, 1965, 1970, and 1973 national championships, seasons in which the winner of the Coaches' Poll went on to lose their bowl game.
Bobby Burnett tied three others in scoring, with 16 TDs, the fourth-highest total in the nation. Ronny South was second in kick scoring, with 42 extra points and 6 field goals. As an offensive unit, the Hogs had the best scoring offense (32.4 ppg), the eighth-best rushing offense (226.1 ypg), seventh-best total offense (360.2 ypg) nationally. The defense was fourth-best against the run (74.9 yards allowed per game).
The Arkansas Razorbacks put their 22-game win streak on the line in the 1966 Cotton Bowl Classic against their rivals, the Tigers of LSU. Arkansas had the number-one scoring offense coming into the game, averaging 32.4 points per contest.
Arkansas took the ball to the end zone on the opening drive, capped by a 19-yard toss from Jon Brittenum to All-Americanend Bobby Crockett. Running back Joe LaBruzzo then ran in from three yards out for the Bengal Tigers to tie the game at 7. Razorback QB Brittenum then left the game after suffering a shoulder injury and the Hogs fumbled the ball three plays later. LaBruzzo again scored, this time from one yard away, giving the Tigers a 14–7 halftime lead.
Neither team scored in the second half, and Arkansas ended the game on the LSU 24-yard line. Razorback Bobby Crockett set a bowl record with 10 catches for 129 yards.
Georgia's number-one ranked defense matched up against Arkansas ninth-ranked offense on New Year's Day in New Orleans.
Razorback QB Bill Montgomery led the only scoring drive, capped with a 23 yard strike to Chuck Dicus. Georgia responded with David McKnight tackling Razorback Bill Burnett in the end zone for a safety, after which Razorback kicker Bob White took over, adding three unanswered field goals. The game ended with a 16–2 Razorback win. Chuck Dicus caught twelve passes for 169 yards and a score, and was named player of the game.
Bill Burnett scored 20 touchdowns, the third-highest total in the nation. Kicker Bill McClard tied Happy Feller of Texas with 61 points scored, 40 extra points and 7 field goals. As a team, Arkansas had the #1 defense, allowing only 7.6 points per game.
With two legendary coaches (Broyles and Royal), two neighboring states, two football powerhouses (8 of last 10 SWC Championships), and two recent National Championships (Arkansas in 1964 and Texas in 1963), Arkansas and Texas had developed a rivalry. The game was moved from the usual third week in October to the first week in December so it could be televised nationally on ABC. President Richard Nixon attended the game, and AstroTurf was even installed in Razorback Stadium in preparation for the game.
Arkansas' top-rated defense was going up against the #1-rated Texas offense, but the Hogs got on top early, with a 1-yard TD run by Bill Burnett. After halftime, Chuck Dicus hauled in a 29-yard touchdown pass, giving the Razorbacks a 14–0 lead heading into the game's final quarter. Longhorn QB James Street then led his squad to its first touchdown, and as coach Darrell Royal had planned, Texas attempted and completed the two-point conversion, which would in all likelihood prevent a tie.
Arkansas then had the ball and the lead, and a 73-yard drive later, the Hogs were in good position to tack on a field goal that would put the game out of reach, but Razorback QB Bill Montgomery was intercepted in the end zone, giving the Longhorns new life. The Texas drive appeared stalled at the Longhorns' own 43, on a 4th and 3, when Royal gambled again. A 44-yard pass to Randy Peschel, who caught the ball in double coverage, put Texas at the Arkansas 13. Longhorn RB Jim Bertelsen would run in for the tying six points. The extra-point snap was high, but was snared by third-string QB Donnie Wigginton and the kick was converted by Longhorn kicker Happy Feller, giving Texas a 15–14 lead with 3:58 to play.
Arkansas drove to the Texas 40, looking for a field goal from All-American kicker Bill McClard, but the turnover bug struck again as Montgomery was again picked off.
Ole Miss RB Bo Bowen scampered 69 yards to open the scoring, with Archie Manning adding another 18-yard TD run. Down 14–0, Arkansas responded with a 12-yard TD run by Bill Burnett, but the extra point was missed, and after a Rebel field goal and Archie Manning 30-yard TD strike, were down 24–6. Before halftime, Chuck Dicus hauled in a 47-yard pass from Bill Montgomery, but the two-point conversion was incomplete, and the Rebels took a 24–12 halftime lead.
The third quarter produced a field goal from each team, and in the fourth quarter fullback Bruce Maxwell caught a six-yard strike from Montgomery to cut the lead to five, but the rally fell short, the Hogs losing by a 27–22 final.