Jordan Pacheco added two hits and two RBI in his first major league game, while Seth Smith went 3-for-4 with two triples and two runs scored for the Rockies, who had lost two in a row including Monday's series opener.
Matt Belisle (10-4) picked up the win by notching the final out of the eighth.
"It's nice to get a win, especially a come-from-behind one," Tulowitzki said. "There are some new guys on the team. It's nice to get them off to a good start."
David Hernandez (3-3) was charged in defeat for five runs on five hits and recording only two outs.
Colorado forged ahead for good in the eighth against Hernandez. Pinch-hitter Kevin Kouzmanoff started the rally with a one-out single, but was erased on a Dexter Fowler fielder's choice. Mark Ellis followed with a base hit and Carlos Gonzalez plated Fowler on a single to bring the Rox within 3-2.
Both runners advanced on a passed ball, then Tulowitzki managed to muscle a ball over the wall in left-center to make it 5-3 for the home squad. Ty Wigginton singled, and after Hernandez was tossed from the game by home plate umpire Todd Tichenor, Wigginton scored on a triple from Smith against Joe Paterson. Wilin Rosario followed with a walk, ahead of Pacheco's RBI single.
"I usually don't show emotion, but when you lose a ball game, it adds a little," Hernandez said.
Sam Demel came on and plunked Kouzmanoff to load the bases, and Fowler drew a walk to force in a run to make it 8-3 before Ellis flied out to end the rally.
Rafael Betancourt set Arizona down in order in the ninth.
Smith began the fifth with a triple and scored two batters later on a Pacheco groundout.
Paul Goldschmidt doubled to start the Arizona seventh, moved to third on a passed ball and scored on a one-out single from Parra.
It was 3-1 for the visitors in the top of the eighth after Hill doubled with one out against Huston Street and scored when Pacheco threw wild to first on a Montero infield hit against Matt Reynolds. Belisle came on to retire Goldschmidt on a fly to right.
Colorado starter Jason Hammel allowed six hits and two runs -- one earned -- with six strikeouts in seven innings, while his Arizona counterpart Josh Collmenter lasted 6 1/3 innings, scattering five hits and one run with four strikeouts...Despite the loss, Arizona still leads the season series, 12-5, winning five of eight in Denver...Prior to the game, the Rockies announced that infielder Jonathan Herrera will miss the remainder of the season due to a fracture of his right index finger. Herrera, who suffered the injury when he shut a door on his hand over the weekend, was put on the 60-day disabled list.