The first Cardinals starter to go 10 innings since Jose DeLeon pitched 11 against Cincinnati in 1989, Mulder threw only 101 pitches in his ninth career shutout.
"I wasn't tired, but they would have taken me out for a pinch-hitter in the ninth if my spot had come up," he said.
Mulder (2-1) enjoyed the 43-degree weather and won his second consecutive outing after going winless in his first two starts.
"I like it when I'm the only one sweating out there," he said. "I'm pitching the same way I always have, I'm just getting better results."
Larry Walker's RBI single off Brad Lidge in the 10th won it for the Cardinals, moving manager Tony La Russa into a tie with Joe McCarthy for fifth place on the career victories list at 2,125.
Clemens allowed four hits in seven innings, lowering his ERA to 0.32 and pushing his scoreless streak to 23 innings. But he was thwarted for the third straight time in his bid for his 330th win. He remains tied with Steve Carlton for ninth on the career list.
The Astros have not scored a run for Clemens in 22 innings. They did not even put a runner on third base in this one.
"I don't worry about that side of it," Clemens said. "I was moving the ball around and I got out of a few spots."
Mulder set a career high for innings pitched, giving up four hits, striking out five and walking none in his 23rd complete game. The lanky left-hander, acquired from Oakland in an offseason trade, lowered his ERA from 4.74 to 3.10.
"He pitched a pretty decent game, but we swung at a lot of balls," Astros manager Phil Garner said. "We need to be a little better selective the next time out."
Mulder has not allowed an earned run in his past two starts, giving up just six hits in 18 innings.
Pinch-hitter Reggie Sanders led off the 10th with an infield single against Chad Qualls (1-1). After Sanders moved to second on a groundout, Lidge came in to face Walker, who lined a single to left to score Sanders.
"It was a swinging bunt that feels just as good as a ringing line drive," Sanders said. "I was enjoying the game from the bench and I'm glad I was part of the win."
Lidge said Walker hit a good pitch.
"It was a fastball, down and away and he reached for it. I'm not upset about the pitch at all," he said.
Clemens, who threw 126 pitches, had six strikeouts and a season-high four walks. He and Mulder were facing each other for the first time in a regular-season game. They were the starting pitchers in last year's All-Star game.
In six career starts against the Cardinals, Clemens is 3-0 with a 2.43 ERA. That doesn't include the 2004 postseason, in which Clemens lost Game 7 of the NL championship series at Busch Stadium.
The Cardinals loaded the bases with two outs in the third, but Roger Cedeno, who had been 10-for-24 against Clemens, grounded out to end the inning.
- LF Chris Burke robbed Mulder of a hit with a diving catch in the fourth.
- Mulder shook off the effects of being struck on the left ankle by a piece of Mike Lamb's shattered bat in the fourth.