In Groh's last game, Randolph faced off against Montclair High School on December 1, 1990 in the New Jersey North 2, Group 4 sectional championship game, which was held at Woodman Field in Montclair. Randolph had entered the game sharing a state record for consecutive victories with 48 while Montclair was the top ranked team in the state and fifth in the United States. With his team trailing 21-19 and driving late in the game, Randolph turned the ball over deep in Montclair territory. Montclair attempted to run the clock down as far as they could, with the idea that they would take a delay of game penalty and have approximately three seconds left to punt the ball. However, a clock error resulted in the scoreboard clock ticking to zero and caused the Montclair fans to rush the field in apparent victory. This not only resulted in a delay of game penalty being called on Montclair, but the officials determined the clock should have seven seconds left on it. After Montclair came up with an eleven-yard punt that was fair caught with a second left, Groh kicked the winning field goal as time expired to give Randolph its record breaking victory in what The Star-Ledger of Newark later named the greatest New Jersey high school game ever played.
Groh enrolled at the University of Virginia in the fall of 1991 and was redshirted as a true freshman. He served as a backup quarterback during his redshirt freshman season in 1992 and replaced struggling starter Bobby Goodman in a late season game against N.C. State. However, in the 1993 season, Groh lost the quarterback competition to fellow redshirt sophomore Symmion Willis and again served as a backup. In the first game of the 1994 season against Clemson, Groh alternated with Willis when the offense struggled during a 6–3 win. Groh and Willis continued to alternate at quarterback for the next few games until Groh emerged as the starting quarterback. The Cavaliers finished 9–3 for the 1994 season with a win over Texas Christian University in the Independence Bowl. Groh led the Cavaliers to a 9–4 record in the 1995 season highlighted by a 33–28 win over Florida State and a win over Georgia in the Peach Bowl. His father is Al Groh, who served as the head football coach at Virginia after Mike had graduated.