Walton's point total was a career high. Sophomore guard Caris LeVert supplied 17 points for Michigan (15-4 overall, 7-0 Big Ten), which has won nine straight.
The Wolverines, who scored 10 straight points during a late stretch to take command, relied on their outside shooting, making 11 of 19 3-point attempts.
Sophomore guard Gary Harris had a career-high 27 points for Michigan State (18-2, 7-1). Freshman guard Alvin Ellis III added 12 points and freshman center Matt Costello posted career highs with nine points and nine rebounds.
The Spartans played without their two best frontcourt players. Adreian Payne missed his fifth consecutive game because of plantar fasciitis in his right foot and Branden Dawson broke his right hand during a film session on Thursday.
A Harris 3-pointer gave Michigan State its biggest lead of the second half at 49-41. Things then got a little heated when Spartans forward Russell Byrd blocked a shot by Michigan forward Glenn Robinson. Wolverines center Jordan Morgan and Spartans guard Keith Appling received technicals.
Moments later, LeVert tied it at 53 with a 3-pointer. Appling's layup eventually put the Spartans back on top, 60-58, but Michigan then went on its decisive spurt.
Stauskas' transition 3-pointer gave the Wolverines the lead and Walton's three-point play with 2:29 remaining made it 66-60. Two Walton free throws with 1:58 left pushed Michigan's lead to eight.
Michigan State got as close as three in the closing seconds, but LeVert free throws iced the Wolverines' victory.
Harris' 12 first-half points, including a fast-break layup in the closing seconds, helped the Spartans take a 36-30 halftime lead.
Michigan State recovered from a quick eight-point deficit by shooting 52 percent from the field in the opening half.
Michigan stayed close by making 6 of 11 3-point shots before intermission.
NOTES: This was the first meeting between the teams when both were at least 6-0 in the Big Ten. It was also the fifth consecutive meeting when both were ranked. ... Michigan State's best conference start was a 9-0 record in 2010. Michigan won its first 13 Big Ten games in 1964-65. ... The Spartans won 20 of the last 27 meetings but had lost four of the last six. The home team won the last five times. ... The Wolverines had not played three consecutive Top 10 opponents since December 1963. It defeated then No. 3 Wisconsin and No. 10 Iowa in its previous two games. ... Michigan State used its 10th different lineup in the last 15 games. ... The rematch in Ann Arbor will be played Feb. 23. ... Wolverines G Nik Stauskas has a Big Ten-leading nine 20-point games. ... Spartans G Gary Harris has scored in double figures in every game he has played this season.