CHICAGO — Adam Wainwright called the most recent homestand a reality check for St. Louis. He’s not quite ready to call this a turning point for the Cardinals.

Matt Carpenter and Matt Holliday homered to back Wainwright, and St. Louis beat the Chicago Cubs 4-3 on Tuesday night.

The Cardinals won their second straight game after going 0-5 on their first winless homestand of at least two series since 1983.

“I think a reality check set in where we’re going to have to learn how to win and play in those close games better,” Wainwright said. “When we come in here to this great city and this great team, we’re going to have to play some tough games, some close games, and you’re going to have to learn how to win those games.”

The Cardinals made it consecutive one-run wins over the Cubs after three straight one-run losses to Texas. And while Wainwright called it an “overstatement” to “say this is a statement series,” there are certainly some promising signs coming from St. Louis.

Carpenter and Holliday connected against Jason Hammel (7-3) in a three-run third inning that made it 4-1. Wainwright (6-4) pitched into the seventh and improved to 10-1 in 21 games — 16 starts — at Wrigley Field.

The Cardinals put themselves in position to sweep their first trip to Chicago since last year’s NL Division Series, though it won’t be easy with the major league-leading Cubs sending reigning NL Cy Young Award winner Jake Arrieta to the mound.

“They’re really, truly buying into the idea that we’ve got to look like the kind of team that we should do that,” manager Mike Matheny said. “When we do that, we’ll throw ourselves in the ring with anybody.”

Chris Coghlan scored two runs for Chicago, whose longest losing streak is three games. The only other time the Cubs dropped two straight at home was when San Diego swept a doubleheader on May 11. But they came up short in this one, hitting into three double plays and going 0 for 9 with runners in scoring position.

“I have no complaints about the last two nights — zero,” manager Joe Maddon said. “We played well. We played good baseball.”

Wainwright allowed three runs and six hits in 6 2/3 innings.

Chicago’s Addison Russell doubled off the wall in left leading off the seventh. Jonathan Broxton came in with two outs and walked Coghlan, putting runners on first and third, but first baseman Brandon Moss made a diving stop on Jason Heyward’s grounder to end the threat.

Kevin Siegrist worked the eighth, and Trevor Rosenthal handled the ninth for his 14th save in 16 chances. Shaky in Monday’s win, he gave up a one-out single to Russell and walked Javier Baez with two outs before pinch-hitter Matt Szczur grounded into a force play to end the game.

Hammel went 5 2/3 innings, allowing four runs and six hits.