The Cornhuskers' effort gives coach Doc Sadler reason to hope better days are ahead for the Big Ten newcomers.
"This team is going to win some ball games. I believe that," Sadler said. "As long as we continue to compete, we're going to have some shots at it. We have to figure out how to finish it off. You're at home with a four- or five-point deficit last 4-5 minutes, you have to figure out how to win it. We had some opportunities. We just didn't capitalize."
The Spartans (13-2, 2-0 Big Ten) won their 13th straight game and are on their longest streak since the 1998-99 team won 22 straight. Eleven of the 13 have been by double digits.
Nebraska (8-5, 0-2) started conference play with consecutive losses for the second time in three years after losing to No. 11 Wisconsin and Michigan State. It is the first time since 2001-02 that the Huskers faced ranked teams in their first two conference games.
The Spartans proved too powerful inside against a Nebraska team that was without 6-foot-11 center Jorge Brian Diaz (sore feet) for a fourth straight game. The Huskers also were missing their fourth-leading scorer, guard Dylan Talley (thigh bruise).
The Huskers still turned in a game effort despite shooting 36 percent and getting outrebounded 38-24.
"That team plays with energy like that, they're going to win some games," Michigan State coach Tom Izzo said. "Don't look past the Wisconsin game. Wisconsin can do that to a lot of teams at times, especially the first Big Ten games. If they can stay healthy... that's what I feel bad about for Doc."
Michigan State finished on a 15-5 run after Nebraska (8-5, 0-2) pulled within 53-50. The Huskers made just one field goal over the last 6:48.
Austin Thornton's 3-pointer made it 62-55, and Huskers didn't make a field goal over the last 4:20.
"We knew they were going to make runs, we knew we were going to make runs, and we got down to that point," McCray said. "We were saying, 'This is what we prepared for all week. This is when the game really starts.'
"I've been here for five years, and I've seen this all the time in league play. You get down to something like that where you're up five, down five; up three, down three, and whoever executes and does what they're supposed to do and gets their assignments the best is who's going to win."
Michigan State has won its first two Big Ten games for the fifth straight season. Nebraska is in the middle of a stretch of eight games in which six opponents are ranked in the Top 25.
The slow-starting Spartans missed 8 of their first 9 shots, never led in the first half and were down 30-29 at the break. But 6 ½ minutes into the second half they were up by 15 points and looked ready to run away with the game.
Nebraska didn't fold. Michigan State went 4 ½ minutes without a field goal, Spencer's 3-pointer finished a 16-4 run that pulled the Huskers to 53-50 with under 9 minutes to play.
Appling scored six straight points to build the Spartans' lead to 59-50, but Nebraska came back again. McCray hit a 3-pointer and Spencer made two free throws to make it 59-55 with 4:01 left.
Nebraska's offense stalled after Thornton's 3-pointer gave the Spartans a seven-point lead. Caleb Walker missed a 3 from the corner, Brandon Richardson committed a turnover and Green blocked Walker's 3-point try.
The Spartans didn't take their first lead until their opening possession of the second half, when Appling drove the lane to start a 18-4 run.
The Huskers opened the game much the way they did on Tuesday against No. 11 Wisconsin, when they carried the play before getting worn down and losing 64-40. They didn't cave so quickly this time.
"We're all coming to practice on the same page," Spencer said. "This isn't my first time coming into a season where we've been kind of looked at as the underdogs or something. We'll keep fighting, keep playing. We'll turn it around."