With 1:02 left, Vikings quarterback Daunte Culpepper threw a near-perfect pass to Randy Moss in the end zone, but Tillman jumped with Moss and ripped the ball out of his hands to prevent Minnesota from scoring the go-ahead touchdown.
The Vikings (8-6) have lost six of their last eight games to lose their grip on the NFC North.
Grossman completed only 13-of-30 passes for 157 yards, but kept the offense running smoothly for Chicago (6-8). In his NFL debut, the first-round pick out of Florida guided the Bears to a turnover-free game.
Anthony Thomas scored the only touchdown for the Bears, who have won three of their last four games.