A native of Cleveland, Ohio, Putich played only 13 minutes of a possible 540 as a sophomore in 1949. He earned the nickname 'One-Play-Putich' in Michigan's 7–3 win over Michigan State in 1949; Putich appeared for only one play in the game, throwing a touchdown pass to win the game.
Putich took over as the starting quarterback for the 1950 Michigan Wolverines football team. After a 14–7 loss to Michigan State in his first start, some questioned his selection as the starting quarterback. Sports writer John F. Mayhew wrote a column in defense of Putich, noting that he was inexperienced but showed promise. Mayhew noted:
Putich is an eager, hard-working, intelligent football player. He's good enough to have the complete faith of Backfield Coach George Ceithaml, one of Michigan's best quarterbacks and a man who should really know. Given a reasonable break, he'll prove it too.
Putich proved Mayhew correct in leading the 1950 team to a 9–3 win over Ohio State in the famed Snow Bowl game, a Big Ten Conference championship, and a 14–6 win over the University California in the 1951 Rose Bowl. The 1950 team was ranked No. 9 in the final Associated Press poll and No. 6 in the coaches' poll.
In February 1951, Putich was ruled ineligible to compete for Michigan's basketball team due to academic deficiencies.
In the fall of 1951, with his eligibility restored, head coach Bennie Oosterbaan moved Putich from the quarterback position to the left halfback position. Putich was also the captain of the 1951 team. An October 1951 feature story "Three P's Put PUNCH in Michigan Attack," Putich was described as a "hard-driving and tricky runner."
Putich's career totals at Michigan included 668 yards passing with his longest pass completion of 55 yards against Minnesota in 1951. He also had 206 net yard rushing, 153 yards on pass receptions, and 212 yards on punt and kickoff returns.
- John F. Mayhew (1950-10-04). "Bill Putich Is Defended By Writer". News-Palladium.
- "Three P's Put PUNCH in Michigan Attack". Iowa City Press-Citizen. 1951-10-19. (The other two "P's" profiled in the story were end Lowell Perry fullback Don Peterson.)
- "1950 Football Team". Bentley Historical Library, University of Michigan.
- "Bill Putich Ineligible, Draftable; U-M Quarterback Benched for Season". Detroit Free Press. February 3, 1951. p. 12.
- Tommy Devine (September 25, 1951). "Daring Move: Putich's New Spot Is Big U-M Gamble". Detroit Free Press. p. 18.
- "1951 Football Team". Bentley Historical Library, University of Michigan.
- Lloyd Northard (1951-09-22). "Bill Putich Given Michigan Signal-Calling Spot for 1951: Oosterbaan Plugs Offensive Holes". Waukesha Daily Freeman (AP story).
- "Putich Named M Grid Captain: But Army May Take Quarterback by Autumn". Detroit Free Press. January 24, 1951. p. 17.
- Hal Middlesworth (October 15, 1951). "Putich, Peterson Provide M's Punch". Detroit Free Press. p. 28.
- "Michigan Football Statistic Archive Query Page". University of Michigan. Archived from the original on 2007-11-12.