As a sophomore, Glinka played in all nine games at quarterback, three as a starter, for the 1960 Michigan Wolverines football team.[4][5][6] He was the first sophomore to start as Michigan's quarterback since Forest Evashevski in 1938.[7][8][9] He made his debut as Michigan's starting quarterback in the season opener against Oregon. Glinka completed 5 of 11 passes against Oregon and threw two touchdown passes (to George Mans and Scott Maentz) to lead the Wolverines to a 21–0 victory.[4][10] Against Michigan State in the second game of the 1960 season, Glinka completed 6 of 19 passes for 96 yards.[4] In the third game of the 1960 season, Glinka led the Wolverines to a 31–6 win over Duke. Glinka completed 8 of 14 passes for 111 yards.[4] On the first drive of the second half against Duke, Glinka led the Wolverines to a touchdown with passes of 34 yards to Scott Maentz, 11 yards to Bob Johnson and 5 yards to Dennis Fitzgerald.[11] In week four, Glinka led Michigan to a 14–7 win over Northwestern, throwing a 50-yard touchdown pass to Bob Johnson; Johnson caught three of Glinka's passes in the game for 97 yards.[4] In the fifth game of the season, Glinka was intercepted twice in 10–0 loss to Minnesota. In the sixth game, Glinka completed 7 of 18 passes in a loss to Wisconsin. During the 1960 season, Glinka completed 54 of 124 passes for 755 yards and five interceptions. However, he also threw 11 interceptions in nine games.[4]
1961 season
As a junior in 1961, Glinka again appeared in all nine games for the Wolverines.[12][13] Glinka had his best game in a 16–14 victory over Purdue in October 1961. Glinka completed 9 of 11 passes for 170 yards, including a game-winning 72-yard touchdown pass to Bennie McRae in the third quarter.[14] After the game, Michigan head coach Bump Elliott said, "He really came through out there. It was his best day."[15] Three weeks later, Glinka had another strong showing in 28–14 win over Duke. Glinka was four-for-eight passing and threw two touchdown passes, including a 45-yard touchdown pass to Robert Brown.[4] And on November 18, he ran 44 yards for a touchdown in a comeback victory over Iowa.[16] During the 1961 season, Glinka completed 46 of 96 passes for 588 yards, five touchdowns and five interceptions.[17]
1962 season
As a senior in 1962, Glinka began the season as Michigan's No. 1 quarterback.[18] An Associated Press story in the spring of 1962 touted the strength of Michigan's quarterbacking corps and said of Glinka: "No. 1 quarterback, of course, is the ever-improving Toledo senior Dave Glinka. He's in solid with his bosses after two seasons as the leading signal caller. Michigan has been 5-4 and 6-3 in those seasons."[19] After being switched to defense,[20] Glinka was injured in the fourth game of the season against Purdue, underwent knee surgery on October 23, 1962, and missed the remainder of the 1962 season.[21][22]