Detroit blew an 11-point lead over the final 5 minutes but then rallied behind Prince, who finished with 20 points and connected on a pair of key foul shots with 10.9 seconds left.
He had earlier forged a 94-94 tie on a hook shot with less than a minute to play.
Monta Ellis pumped in 30 points and distributed nine assists for the Bucks, who lost for the first time in three games.
Ersan Ilyasova chipped in 24 points for Milwaukee.
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