The Rockies ended a four-game skid with Jhoulys Chacin (10-5) getting the win by allowing a run on six hits over eight innings.
Colorado scored three times in the sixth to take a 4-1 lead. Dexter Fowler walked to open the inning, took third on a single by Corey Dickerson and scored on the base hit by Tulowitzki.
Todd Helton added a two-run single in the inning and Chacin protected the lead by retiring the next nine men he faced.
Rex Brothers allowed back-to-back doubles that produced a Pittsburgh run in the ninth, but he still managed to pick up his eighth save.
Tulowitzki opened the Colorado scoring with a second-inning home run.
Gerrit Cole (5-5) took the loss, giving up three runs on three hits in 5 1/3.