Alvarez socked a solo homer in the second inning and a two-run shot in the ninth, driving in three runs. McGehee added a two-run homer and four RBI for Pittsburgh.
Alex Presley also went deep as the Pirates snapped a four-game losing streak while evening their three-game set at Progressive Field.
A.J. Burnett (7-2) won his sixth straight start, yielding two runs on six hits and four walks over 6 2/3 innings. The right-hander struck out two.
Tribe starter Ubaldo Jimenez (6-5) allowed four runs on seven hits in a six-inning start.