Maryland's leading scorer, Anthony Cowan, was held to a season-low seven points.
The Terrapins connected on just 34 percent of their shots against the Spartans after shooting 58 percent of in their previous game, a 14-point win at Ohio State.
Michigan State freshman Aaron Henry scored a season-high 12 points while Matt McQuaid and Xavier Tillman had 10 points apiece.
Bruno Fernando had 12 points and 13 rebounds, freshman Aaron Wiggins had a season-high 15 points and Darryl Morsell added 10 points.
The Spartans missed their first six shots then surged to an 18-6 lead while holding Maryland to 3-of-18 shooting.
Maryland started making shots to pull into 20-all tie before Michigan State closed half with an 11-0 run to lead 31-20.
Winston, who had just five points in the first half, opened the second half with a 3-pointer to put the Spartans ahead by 14. He had a three-point play a couple minutes later, giving Michigan State a 43-26 lead. Goins made a 3-pointer to push the lead to 22 with 15:28 left.
Maryland: Cowan crumbled against Michigan State's defense. He had scored 20-plus points in four straight games and was averaging 17.9 points entering the game before being held nearly 11 below his average on 3-of-12 shooting. Cowan made a shot early in the game then was held scoreless for 26-plus minutes.
UP NEXT
Maryland: Gives up home game to play Illinois at Madison Square Garden on Saturday.
Michigan State: Plays at No. 19 Iowa on Thursday night and at Purdue on Sunday afternoon.