The rookie allowed six hits and struck out two in seven strong innings to help the Cubs beat the Astros 1-0 on Wednesday night, averting a three-game sweep.
Oswalt struck out six and scattered eight hits in what manager Phil Garner said was the ace's best start of the season.
The loss seemed to be the only thing that mattered to Oswalt afterward.
"You do all you can do," he said. "Hopefully, it will turn around sometime."
Marshall (5-7), meanwhile, snapped a two-game losing streak with his second sharp effort in Houston in a month. On June 7, he gave up only four hits with five strikeouts, but Astros rookie Chris Sampson dominated the Cubs in Houston's 1-0 win.
Marshall mused that the controlled atmosphere in the enclosed ballpark might be the reason for his success here.
"I don't know if it's the roof or what, but the last two starts here, I've pitched pretty well," he said. "I don't know if it's the air conditioning. But I felt good and I didn't want to lose this."
The Astros helped him on Wednesday by stranding 12 runners, including two in the bottom of the ninth.
"I was nervous," said Dempster, who'd blown five of his last 10 save chances. "I was scared of what might come crashing down on me. I can't tell you how big that was for me."
The Cubs won for the third time in 13 games, while the Astros had a four-game winning streak snapped.
Chicago's victory came hours after manager Dusty Baker met with general manager Jim Hendry to discuss the direction of the team. Hendry said he would re-evaluate the team and consider staff changes over the All-Star break.
Baker was confident he would still have his job afterward -- and the victory sure won't hurt his chances.
"This is good for everyone's psyche," Baker said.
Oswalt, a 20-game winner the past two seasons, hasn't earned a victory since beating the Cubs 5-4 on June 14. He has only two wins since May 3, getting no-decisions in five of his last seven starts.
The Astros had scored at least seven runs in their last four games, but Oswalt thinks his teammates tighten up when he pitches.
"I think sometimes they try too hard," Oswalt said. "Instead of just swinging at the ball, like nobody's on, they try to feel for the ball and try to do something with it instead of just swinging."
Marshall allowed only singles to Craig Biggio and Burke until Jason Lane doubled with one out in the fourth. It was Lane's third hit in 17 at-bats, but he was promptly tagged out on Eric Bruntlett's weak grounder back to Marshall.
Walker's double to the wall scored Michael Barrett, who singled with one out. Preston Wilson quickly fielded Walker's liner to the gap and Bruntlett had a chance to throw out Barrett, but his throw home was well off target.
The Astros had plenty of chances to tie it.
They stranded two runners in the first, third and fourth and then loaded the bases with two outs in the fifth. But Lane flew out to Juan Pierre at the wall in left-center.
Biggio led off the sixth with a double off the left-field wall. Burke bunted him to third, but Marshall retired Ensberg and Lance Berkman on groundouts.
"Oh, boy, it was a furstrating night," Garner said. "We had some at-bats where we hit the ball and didn't get anything for it. We had guys all over the bases, with chances to do something. We just didn't do it."
Biggio has 630 doubles, ninth on the all-time list and 10 behind Honus Wagner. He has four straight multi-hit games and 22 this season. ... Berkman had a nine-game hitting streak snapped. ... Oswalt dropped to 10-2 when he pitches a complete game. ... Brad Ausmus ended an 0-for-40 slump with a grounder that ricocheted off a diving Ramirez. Ausmus' hit drought was an Astros' record for a non-pitcher. ... The Cubs have never been swept at Minute Maid Park. The last time they were swept in Houston was in 1999, the
final year the Astros played in the Astrodome.