Colorado ended a six-game losing streak, producing seven runs in the fourth and fifth innings to overcome an early deficit.
The Rockies trailed 4-3 heading into the fifth, but staged a two-out rally against starter Carlos Zambrano (2-3).
Ramon Hernandez led off the inning with a walk, but the next two batters were retired. Marco Scutaro then singled Hernandez to second and a base hit by Carlos Gonzalez delivered Hernandez with the tying run.
That brought up Tulowitzki, who hit a 1-0 pitch over the wall in left for his sixth homer of the season. Tulowitzki also had an RBI double during Colorado's three-run fourth.
Alex White (1-3) survived six innings to get the win, giving up four runs on eight hits. It was White's fourth victory in 15 major league starts spread over two seasons.
Miami had won its previous three games.
Celebrity Families of 2014 [PHOTOS]