He batted and threw left-handed, and was nicknamed "Sweet Music" – a nickname he picked up after a Minnesota sports writer declared that when Viola pitched, there was "Sweet Music" in the Hubert H. Humphrey Metrodome. The nickname was a play on the fact that his last name is also a name of a musical instrument, although pronounced differently. A fan began displaying a banner bearing the phrase in the outfield's upper deck whenever Viola pitched. Twins fans considered the banner to be a good luck charm. The banner is now property of the Minnesota Historical Society. It was again displayed when Viola was inducted into the Twins Hall of Fame. Frank was honored as a member of the Twins' "All Dome" team in 2009.
Viola signed with the Minnesota Twins after the team drafted him in the 2nd round of the 1981 Major League Baseball Draft. After spending less than a full season in the minor leagues, Viola made his major league debut on June 6, 1982. Although his statistics were fairly disappointing, finishing 11-25 with a 5.37 ERA in the 1982 and 1983 seasons, Viola became a permanent fixture of the Twins' starting staff for the next 7 seasons, picking up 112 of his 176 career wins.
Viola helped pitch the Twins to their second World Series appearance and first World Series win in 1987, finishing the season 17-10, with a 2.90 ERA and 197 strikeouts in 251 2/3 innings. Viola would then sparkle in the post-season, going a combined 3-1 with 25 strikeouts in 31 1/3 innings despite a 4.31 ERA. Following the Twins' Game 7 series clinching win, a game which Viola won 4-2, he was named the 1987 World SeriesMost Valuable Player).
Most baseball enthusiasts agree that Viola's best year was 1988, his last full year with the Twins. That year, he threw his signature circle change with skill, compiling an impressive 24-7 record, with 7 complete games and 2 shutouts in 255 innings pitched with a career-low ERA of 2.64. He also gave up only 20 home runs, and 54 walks. Viola led the league in wins and would go on to win the AL Cy Young Award in a landslide, finishing with 27 of the 28 first place votes and beating out 2nd place Dennis Eckersley by 86 total votes.
At the trade deadline in July 1989, two years after Viola had led the Twins to a World Series title, the Twins traded him to the New York Mets for four pitchers and a player to be named later. Viola was not having a strong year and was 8-12 when he was traded, but managed a 5-5 record with the Mets and finished the year at 13-17. Meanwhile, two of the pitchers the Twins acquired in the deal went on to become key members of the team, as Kevin Tapani was one of the front line starters for the Twins in their 1991 World Series run while Rick Aguilera eventually became the team's closer and one of the better relievers in the major leagues.
Viola had a much better year in 1990, winning 20 games for the second time in his career. He would finish third in the Cy Young Award voting behind Pittsburgh's Doug Drabek and Los Angeles' Ramón Martínez, and was named to the National League's All-Star Team.
In 1991, Viola made the All-Star Game for a third time after posting an 11-5 record in the first half of the season. However, as the Mets collapsed in the second half of the year to finish with a 78-84 record, Viola collapsed with them and went 2-10 in his final 12 decisions. His last win came in his second to last start with the Mets, on September 29 at Shea Stadium against the Philadelphia Phillies. He became a free agent after the 1991 season when the Mets opted not to resign Viola.
Game 4 was his second start, and the Twins went on to lose 7-2. After the Twins tied the series in Game 6 with an 11-5 win thanks to a Kent Hrbek grand slam, it was up to Viola in Game 7. He pitched a gem, shutting the Cardinals out after giving up 2 runs in the 2nd inning. Jeff Reardon pitched the ninth inning and the Twins won 4-2 and won the World Series 4-3. Viola was named World Series MVP.
In retirement, Viola for a time coached baseball for Lake Highland Preparatory School in Orlando, Florida. He also coached with the Florida College Summer League's Leesburg Lightning. In 2009, Frank assisted the Cleveland Indians as a coach in spring training. Frank was also a part-time, substitute game broadcast announcer for NESN, network of the Boston Red Sox. On January 26, 2011, Viola was hired as pitching coach of the Brooklyn Cyclones, the Mets' Single-A (Short Season) team. Viola spent 2012-2013 as the Single-A Affiliate Savannah Sand Gnats pitching coach, winning Coach of the Year in 2013. Following the season, Viola was named the pitching coach for the Las Vegas 51s, the Mets' Triple-A affiliate in the Pacific Coast League. During a 2014 spring training physical, Viola was diagnosed with a heart condition that required open-heart surgery on April 2. After surgery he signed with Las Vegas 51s.