Suppan (2-0) allowed one run over five innings to win his second start since he replaced the injured Cory Luebke in the starting rotation. Suppan gave up a run in the first inning before throwing four scoreless innings. He gave up four hits, struck out one and walked two.
Padres manager Bud Black noted Suppan, a 17-year veteran, has been building up his stamina after dealing with a triceps issue during Spring Training. Before he joined the Padres on May 2, Suppan pitched two games at Triple-A Tucson.
"He had a lengthy first inning, but he hung in there," Black said. "He really did. He gave it everything he had through the five innings. He's still, in a sense, working his way into his stuff, into stamina.
"But he's got such a good head on his shoulders. He knows how to change speeds, mix pitches, knows what he can do to get through the opposition's lineup. He's got great pitching instincts."
At the end of the night, Thayer wrapped up the Padres' second consecutive victory with his second save. Thayer has picked up the Padres' two save opportunities since closer Huston Street went on the disabled list for a strained right lat on Saturday.
Thayer struck out Carlos Gonzalez swinging to end Tuesday's game with runners on first and third.
Thayer allowed three hits in the ninth, but struck out two. After allowing a leadoff single to Tyler Colvin, Thayer struck out pinch-hitter Jason Giambi. After Marco Scutaro singled and Colvin advanced to third on an error, the Padres caught another break.
With runners on first and third, Jordan Pacheco's sharp grounder hit Scutaro, who was ruled out, while Pacheco was credited with a single and Colvin was forced to return to third base. Thayer then struck out Gonzalez to earn his third career save.
"That's one of the hottest hitters in the National League, their hottest hitter," Black said. "CarGo came out aggressive.
"They had the right guy up there, I'm sure they thought. Dale just got a couple pitches above the zone. When you're throwing the ball in the low- to mid-90s and you're above the zone, it's tough to catch up
The Rockies scored their lone run in the first inning on Todd Helton's RBI single. Colorado left the bases loaded, as Suppan got Ramon Hernandez to fly out to end the inning.
"It came down to mixing pitches," Black said.
After allowing two hits in the first inning, Suppan held the Rockies to two hits over the next four innings.
"We should have scored more runs off that guy," Gonzalez said. "Every at-bat against him, he put me at 3-0. After that, every pitch was right on the corner, right on the border."
Suppan's ERA is 0.90, as he has allowed one run over 10 innings.
"I had some command issues, but I just kept battling," Suppan said. "The bullpen did a fantastic job making up some innings there and doing well."
Five Padres relievers combined to throw four scoreless innings.
For the Padres, Will Venable went 2-for-4 with an RBI double in the fifth inning that gave the Padres a 2-1 lead. He led off the first with a triple and scored on Yonder Alonso's single to tie the game 1-1.
Orlando Hudson's triple gave the Padres a 3-1 lead in the eighth. He drove in Alonso, who drew a leadoff walk.
Rockies starter Alex White (0-1) allowed two runs in a career-high 6 1/3 innings in his 2012 debut. He struck out five, walked two and gave up six hits.
"I felt good," White said. "I was confident with all my pitches, putting the ball where I wanted to. My goal tonight was to get deep because this bullpen had to throw a lot of innings."