The Gophers (6-4, 2-4 Big Ten) won for the second time in three games and pushed their winning streak at Memorial Stadium to four. Minnesota was content to keep the ball on the ground after completing only three passes in the first half and nine the entire game.
Kirkwood, a sophomore from Delray Beach, Fla., scored on a 3-yard run in the third quarter to break a 3-3 tie. The run capped an 11-play, 51-yard drive.
After Minnesota recovered a fumble by Illini quarterback Nathan Scheelhaase on a quarterback sneak on third-and-1 at the Illinois 29, Kirkwood scored on a 12-yard touchdown run late in the fourth quarter to clinch it.
The game pitted two sluggish offenses which combined for 585 total yards.
Minnesota freshman quarterback Philip Nelson won for the second time in his fourth start, but the Gophers relied on the running game. He threw for just 78 yards.
While Kill's program enjoyed a milestone victory, Illinois continued a slide under first-year coach Tim Beckman.
After losing its final six Big Ten games last season, Illinois (2-8, 0-6) saw its Big Ten losing streak hit 12 games. The Illini have lost seven consecutive games this season.
When Scheelhaase threw an incomplete pass on a fourth and three from the Minnesota 35-yard line with 5:12 left, the Illini failed on their best scoring chance in the second half.
Scheelhaase threw for 175 yards on 15 of 23 passing, but he lost two fumbles.
The Illini managed just 101 yards rushing. Running back Donovonn Young led Illinois on the ground with 42 yards.
Illinois didn't get much done against the Gophers. Illinois took a 3-0 lead on a 20-yard field goal by Nick Immekus in the first quarter after a drive stalled at the Minnesota 2-yard-line.
Besides that early scoring chance, the Illini also had a fumble and six punts in their first eight possessions.
Scheelhaase completed a 49-yard pass to wide receiver Spencer Harris on a flea-flicker on the Illini's first drive, and it looked like Illinois had some early momentum. Illinois couldn't keep it rolling.