Counted out in February, the Tom Izzo-coached Spartans (26-11) are instead headed to the Elite Eight for the second straight year and fourth time since 2009. And they're going as a seventh-seeded team that knocked off the third-seeded Sooners (24-11), a week after knocking off No. 2 Virginia.
Travis Trice led the Spartans with 24 points, while Branden Dawson had 11 rebounds.
Buddy Hield led the Sooners with 21 points.
Michigan State is the lowest-seeded team still in the tournament, and advances to face fourth-seeded Louisville on Sunday.
The game turned once Michigan State took its first lead, going up 44-42 on Dawson's 8-foot turnaround jumper with 9:26 left. The teams traded the lead four times before the Spartans went ahead for good with 6:42 left, when Matt Costello put back his own miss with an emphatic dunk.
After Hield missed a three-point attempt at the other end, Valentine responded by hitting a pull-up three-pointer in transition to make it 51-47.
And Michigan State maintained the lead by finally hitting shots from the free-throw line. After missing seven of their first 10, the Spartans were perfect on their final six free throws.
Trice hit two to put Michigan State up 62-58 with 13.2 seconds left. Hield missed a three-point attempt on what became the Sooners' final possession in a game that stretched into Saturday morning.
The Sooners got off to a blistering start on offense by hitting eight of their first 11 attempts, and built a 18-8 lead on Khadeem Lattin's putback of a Jordan Woodard miss 5 1/2 minutes in. It was an impressive start against a stingy Spartans' defense that had limited Virginia to hitting just 17 field goals in a 60-54 win last weekend.
Oklahoma, however, couldn't maintain the pace and allowed the Spartans back into the game. Valentine missed six of his first seven attempts before hitting a three-point basket with 2:36 left to cut the Sooners lead to 31-27.