The score capped the first drive in which the Spartans really showed the ability to move the ball and Connor Cook found rhythm.
Cook was 3 of 4 passing for 69 yards on the 9-play, 73-yard drive. Cook connected with Lippett for an 18-yard reception on the second play and three plays later, Cook hit MacGarrett Kings down the sideline for a 25-yard gain.
Two plays later, Cook hit Josiah Price on a throwback to the tight end and Price rumbled from the Purdue 33 down to the 7-yard line.
MSU then dialed up a little trickery, with Cook rolling to his left and pitching the ball to Lippett, who ran to his right and found Gleichert open for the touchdown.
Michigan State's defense opened the scoring at 10:17 of the second when Max Bullough came untouched on a blitz and forced an Etling fumble, which Denicos Allen scooped it up and returned it 45 yards for the touchdown.
The Spartans defense had gone four games without a touchdown after having four in the first two games of the season.
It was the first touchdown of Allen's career.
Michigan State shut out the Boilermakers.