McCutchen's shot in the first inning gave the Pirates a 2-0 lead and his blast in the fifth broke a 2-2 tie for Pittsburgh, which evened its three-game series at Comerica Park.
Burnett (2-2) surrendered a pair of runs on seven hits in a six-inning effort. The veteran right-hander walked three and struck out two.
Drew Smyly (1-1) was touched for four runs on seven hits in a 4 2/3-inning stint for Detroit.
Prince Fielder smacked a two-run bomb as the Tigers fell for the sixth time in nine games.