The Rockets (22-10) moved on only after Miami freshman guard Nike Sibande missed a potential game-winning 3-pointer in the final second.
The win could have been costly for Toledo as Tre'Shaun Fletcher, the MAC's player of the year, limped off the floor favoring his left leg. Fletcher finished with 16 points and nine rebounds.
He'll have little time to get ready for Friday's semifinals, where Toledo will play the Eastern Michigan-Akron winner in the second game. Top-seeded Buffalo plays defending champion Kent State in the other semifinal.
Toledo appeared on its way to an easy win, opening a 63-51 lead. However, Miami wouldn't go away and Sibande made a pair of 3s in 10 seconds to pull the RedHawks (16-17) within 70-69.
Sanford, who shot a league-best 89 percent from the line during the regular season, then split a pair of free throws to give Miami one last chance.
Sibande had a decent look from the top of the key, but his shot was just long, allowing the Rockets to escape.
The smooth Sibande led Miami with 20 points and Darrian Ringo had 19.
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