The 11th-seeded Vols (24-13) forced four turnovers in the last 97 seconds including the play when Caris LeVert's foot touched the baseline as he caught an inbound pass with 9.6 seconds to go and Michigan hanging on to a 72-71 lead.
But with a chance to win, Jarnell Stokes was called for a charge, Stauskas made 1 of 2 free throws and Jordan McRae's 70-foot heave wasn't even close.
"I just was there. It's just something I do," Morgan said after scoring 15 points. "I take the charge. That's what I do."
Tennessee was led by McRae with 24 and Josh Richardson with 19, becoming the first SEC team to lose in this year's tourney.
Michigan and Kentucky will meet for the first time since the Wolverines won 81-78 in overtime behind the Fab Five in the 1993 national semifinals.
"Certainly there was a lot of drama at the end," Wolverines coach John Beilein said. "But we've had a lot of that this year."
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