Pierzynski hit a game-tying round tripper in the second inning and Beckham led off the fourth inning with his first home run of the season to help Chicago to its second consecutive win after a five-game losing streak.
Chris Sale (3-1) earned the win with one run on three hits over six innings.
Ubaldo Jimenez (2-2) took the loss in Cleveland's fourth loss in six games. Jimenez lasted 4 2/3 innings and allowed seven runs -- four earned -- on eight hits and six walks.
Shelley Duncan homered and scored two runs to lead the Indians. He doubled in the first inning and scored on an RBI double by Jason Kipnis in the second to give Cleveland the early 1-0 lead.
Chicago tied the score in the bottom of the second and then scored four in the fourth to take command.