"You always want to try and make it as tough for those teams who have something to play for," he said.
Thornburg did just that, tossing six solid innings to lead the Brewers over St. Louis 5-3. Sean Halton homered for Milwaukee, which snapped the Cardinals' five-game winning streak.
St. Louis fell into a tie with Pittsburgh for the top spot in the NL Central. Both teams are 85-61 with 16 games remaining. The idle Cincinnati Reds are 2 1/2 back.
Milwaukee broke a three-game losing streak against St. Louis and beat the Cardinals for only the fourth time in 16 meetings this season.
"It's important to beat these guys. They've been taking it to us pretty good," manager Ron Roenicke said. "We played a good game today. There were a lot of good things that happened."
The Cardinals are 5-1 on their nine-game homestand.
Thornburg (2-1), making his eighth career start, gave up two runs and three hits. He spent most of the season with Triple-A Nashville, going 0-9 with a 5.79 ERA in 15 starts.
Thornburg struck out six and walked two. He has allowed two runs or fewer and gone six innings in all five major league starts this season.
Jim Henderson earned his 25th save in 29 opportunities.
"I thought I threw the ball pretty well," Thornburg said. "I was locating my fastball pretty well. Everything felt good."
St. Louis outfielder Carlos Beltran was impressed with the right-hander.
"The first couple of at-bats you're kind of like wondering, watching what he's trying to do," he said. "We just couldn't do anything against him."
Halton, who had three RBIs, hit a two-run homer off Joe Kelly (8-4) in the fourth to put the Brewers up 4-0. Halton also had a run-scoring single in the second.
The round-tripper was the biggest hit of the season for Halton, a rookie starting his 15th game.
"This is as good as it gets for a guy like me," he said. "Getting called up in September, that's all you can ask for is to be a factor."
Like Thornburg, Halton loves the spoiler role.
"We're in a (pennant) race all right, a race to knock someone else out," he said.
The Brewers jumped on Kelly, who allowed four runs, three earned, on seven hits in five innings. He won his previous five starts, and the Cardinals had won his last eight.
"My stuff felt good, I just missed on a couple pitches," Kelly said. "They didn't hit the ball extremely hard. I just left some pitches up."
Matt Adams hit a two-out solo homer in the ninth, his 13th of the season.
The Cardinals pulled to 4-2 in the fourth on a run-scoring double by Matt Holliday and a sacrifice fly by David Freese. They also put two on with one out in the sixth, but Thornburg retired Beltran and Freese to end the threat.
"We just had a lot of things not really going the way we wanted them to," St. Louis manager Mike Matheny said. "We hit a few balls hard, but (Thornburg) threw a good game against us."
All three games in the series lasted 3 hours, 2 minutes. ... St. Louis RHP Trevor Rosenthal missed the game. His wife, Lindsey, was in labor awaiting their first child. ... Cardinals C Yadier Molina missed his second successive game due to an illness to his mother, Gladys. General manager John Mozeliak said Molina could be back Friday. ... St. Louis 1B Allen Craig is making progress with his injured left foot. "We're still optimistic he'll play again," Mozeliak said. "He's feeling a lot better. It's one of those things where you're just going to have to let some time progress." Craig sustained a left mid-foot strain on Sept. 4. ... The Brewers begin a 10-game homestand Friday against Cincinnati. Kyle Lohse (9-9, 3.59 ERA) will face Reds RHP Mat Latos (14-5, 3.02) in the opener of a three-game series. ... St. Louis ends its homestand with three games against Seattle beginning Friday. Cardinals RHP Adam Wainwright (16-9, 3.03) faces Hisashi Iwakuma (12-6, 2.97).