The Spartans (4-3, 3-1 Big Ten) trailed 7-0 at halftime but rallied against the Wildcats(4-3, 1-2).
Northwestern had won three consecutive Big Ten road games and two straight in East Lansing. But the Cousins-to-White connection wore down the Wildcats.
Cousins hit a wide-open White for a 47-yard touchdown strike to give the Spartans a 14-7 lead with 5:13 left in the third quarter.
White finished with 12 catches for 186 yards and two TDs. Cousins was 21 of 31 for 281 yards.
Northwestern quarterback Mike Kafka completed 34 of 47 passes for 291 yards and two TDs.
Wildcats receiver Zeke Markshausen had 16 catches for 111 yards and a touchdown.
Trailing 7-0 and looking sluggish, Michigan State grabbed the momentum by forcing a turnover early in the second half. Spartans defensive back Chris L. Rucker forced Drake Dunsmore to fumble, and linebacker Adam Decker recovered the loose ball at the Michigan State 36.
The Spartans capitalized with a 64-yard touchdown drive, capped by a 22-yard pass from Cousins to White to tie the score 7-7. Cousins' second TD to White came later in the quarter. Brett Swenson added a field goal as the third quarter expired to put Michigan State ahead 17-7.
Northwestern's Jeravin Matthews fumbled the next kickoff and it was recovered by the Spartans, giving Michigan State good field position to start the fourth quarter. Larry Caper's 22-yard TD run gave the Spartans a 24-7 lead.
Kafka's 1-yard touchdown pass to Markshausen cut the deficit to 24-14 with 10:28 remaining. But Michigan State's defense held the Wildcats scoreless the rest of the way.
Northwestern was at its best early, sapping some of the spirit from Michigan State's homecoming crowd.
Northwestern's defense shone early with a goal-line stand on the game's first possession. The Wildcats stopped Cousins on a fourth-and-inches sneak to keep the contest scoreless.
Wildcats linebacker Quentin Davie ended another Michigan State drive by recovering Edwin Baker's fumble at the NU 20 late in the first half, preserving Northwestern's 7-0 halftime lead.
The Wildcats played without safety Brendan Smith because of a hand injury. The other starting safety, Brad Phillips, suffered what appeared to be a shoulder injury in the first half. Defensive end Corey Wootton played but was limited with an ankle injury.
Northwestern used its no-huddle, quick-pass attack to grab a 7-0 lead midway through the second quarter. Kafka capped a methodical 80-yard, nine-play drive with a 15-yard touchdown strike to Andrew Brewer.