The Pirates scored three times late in the game to erase a 3-2 deficit. After tying the game in the seventh on a Rafael Perez wild pitch, Pittsburgh pushed across a run in the next frame when Andrew McCutchen walked and Garrett Jones singled off Jensen Lewis (2-2), setting up the Alvarez sac fly.
The Pirates added an insurance tally later in the frame when Jason Jaramillo drew a walk and Crosby reached Indians reliever Tony Sipp for an RBI single.
Octavio Dotel hurled a scoreless ninth inning to collect his 14th save and give the Pirates the rubber match of a three-game inter-league set at PNC Park.
Starter Justin Masterson allowed two runs on five hits over six innings of work for the Indians, who dropped their sixth game in seven tries.
Notable deaths of 2014 [PHOTOS]