The Wolverines (4-2, 2-0 Big Ten) got a scare when Robinson left the game with an undisclosed injury late in the first quarter. He missed just one-plus possessions, though, and returned to score on a 6-yard run to put Michigan up 17-0 late in the first half.
Robinson, who wouldn't elaborate on the injury after the game, ran for a 49-yard score - giving him 10,000-plus career yards of offense - on the Wolverines' first drive of the second half and tossed an 8-yard TD pass to Devin Funchess on their next possession to make it 31-0.
The Fighting Illini (2-5, 0-3) lost their starting quarterback, Nathan Scheelhaase, because of an undisclosed injury in the second quarter.
Robinson was 7 of 11 for 159 yards with two TD passes, including one on his first drive to Jeremy Gallon, who turned a short toss into a 71-yard score. He ran 11 times for 128 yards, his 18th career 100-yard game on the ground, and scored on a juke-filled, 49-yard run along with a 6-yard run on a play designed to be a pass.
Scheelhaase completed two passes for 4 yards and ran six times for 34 yards, including a 23-yard gain in which he was injured when he landed face first in the turf when Jibreel Black hit him from behind. He was replaced by Reilly O'Toole, whose two turnovers in the third quarter helped Michigan pull away.
In the first half, Illinois had chances to keep it close.
Illini coach Tim Beckman chose to attempt a 50-yard field goal - instead of going for a fourth-and-4 from the Michigan 32 down by 10 points - and Taylor Zalewski missed the kick, ending the drive in which Scheelhaase was hurt. The Illini turned the ball over on downs on their next possession when running back Donovonn Young was dropped for a loss by Kenny Demens on a fourth-and-1 from the Michigan 41.
The Wolverines turned the lopsided game into a rout with 21 points in the third, turning two turnovers into TDs and forcing the Illini to lose 9 yards in the quarter.
On Illinois' first snap of the second half, O'Toole threw an interception to Demens and the linebacker returned it 13 yards to the Illini 27 to set up Robinson's perfectly lofted pass to Funchess. Toole avoided getting sacked by Jake Ryan later in the third quarter, but held onto the ball long enough for the outside linebacker to get back to him to force a fumble at the Illinois 6.
Fitzgerald Toussaint, who had 62 yards rushing on 18 carries, scored on a 2-yard run two plays later to put the Wolverines ahead 38-0.
Michigan put backup Russell Bellomy, who replaced Robinson when he was hurt, back in and he fumbled on the first drive of the fourth quarter. Bellomy handed off to Thomas Rawls up the middle and he did the rest, breaking two tackles on a 63-yard run to give Michigan a 45-0 lead later in the fourth.
Michigan got its first shutout since beating Minnesota 58-0 on Oct. 1 last season.
Just before kickoff, college football's winningest school unretired the jersey worn by former President Gerald Ford. The Wolverines allowed linebacker Desmond Morgan to wear No. 48 with a "Michigan Football Legends," patch and he made a tackle on Illinois' first play.
Michigan gave its fans a lot of reasons to cheer on a chilly, rainy day, but they were loudest when it was announced that rival Michigan State lost earlier in the day at home to Iowa. The Wolverines will host the Spartans on Saturday, hoping to snap a four-game losing streak in the series.