CLEVELAND -- The game plan for the St. Louis Cardinals offensively is the same every night.

"Relentless at-bats is the goal, regardless of the situation," said manager Mike Matheny after his team produced nine innings of them in an 8-3 win over the Cleveland Indians Tuesday night at Progressive Field.

Left fielder Matt Holliday belted a three-run home run in a four-run eighth inning and designated hitter Mark Reynolds, a former Indian, banged out three hits, to lead a 13-hit assault on six Cleveland pitchers.

The win improves the Cardinals' record to a major league-best 23-9. That's their best start through 32 games since the 1941 Cardinals also started the season 23-9.

All eight of the Cardinals' runs came on two-out hits.

"The strength of our team is we run nine guys out there every day who give good at-bats," said Holliday. "One through nine, the pitcher has to be at his best because we don't give any at-bats away."

St. Louis took an early 4-0 lead but Cleveland cut it to 4-3 in the seventh. The Cardinals rallied for four runs in the eighth against the Cleveland bullpen.

Right-hander Lance Lynn (2-3) started and pitched six scoreless innings to get the win. Lynn gave up four hits and four walks, but no runs, and he struck out nine.

"In big situations, he was able to find a way to get outs," said Matheny.

With one out in the top of the seventh, third baseman Matt Carpenter doubled. Right-hander Carlos Carrasco struck out Holliday for the second out. But shortstop Jhonny Peralta doubled over the head of right fielder Brandon Moss, scoring Carpenter to give St. Louis a 4-0 lead.

Carrasco (4-3) was removed from the game after Peralta's hit. In 6 2/3 innings, Carrasco gave up four runs on 10 hits. He struck seven and did not walk a batter.

"Carlos pitched better than his line showed. But some of it is their guys. They have a really good approach," said Indians manager Terry Francona.

"I thought I did alright. Their first three runs all kind of came on bloops, but that's part of the game," said Carrasco.

The Indians had numerous chances to score in the early innings but failed to get a timely hit. They finally broke through in the seventh inning, which began with a single by shortstop Jose Ramirez off right-hander Matt Belisle, who relieved Lynn to start the inning.

Second baseman Jason Kipnis followed with a double, scoring Ramirez with Cleveland's first run. First baseman Carlos Santana struck out, and left-hander Randy Choate was brought in to face the left-handed hitting center fielder Michael Brantley. Brantley lined a double down the left-field line, scoring Kipnis to make it 4-2.

Pinch hitter Ryan Raburn also doubled to left, driving in Brantley to cut it to 4-3.

In the top of the eighth, Carpenter singled in a run off left-hander Nick Hagadone to extend the St. Louis lead to 5-3. Right-hander Scott Atchison relieved Hagadone, and Holliday belted a 1-0 pitch over the wall in right field for a three-run home run to make it 8-3.

"Holliday's homer was a game changer," said Matheny.

Peralta led off the second inning with an infield single. After first baseman Matt Adams struck out, catcher Yadier Molina singled to right, moving Peralta to second. The runners went to second and third on a groundout before Reynolds' two-run single gave the Cardinals a 2-0 lead.

The Cardinals added a run in the fifth. Reynolds led off with a single and went to second on a single by center fielder Peter Bourjos. Second baseman Kolton Wong popped out to Carrasco on a bunt attempt and Carpenter struck out, but Holliday blooped a single to center to score Reynolds to make it 3-0.

In the bottom of the fifth, Cleveland loaded the bases with one out, but Lynn struck out Brantley and Moss to end the threat.

"That was a big situation, but Lance got out of it by striking out the three-hole hitter in a tough lineup," said Matheny. "Getting those two strikeouts really turned things around."

NOTES: Cardinals 3B Matt Carpenter returned to the team Tuesday after taking off the three-game series in Pittsburgh because of extreme fatigue. ... Indians C Yan Gomes could be close to going on a minor league rehab assignment. He has been on the disabled list since April 12 with a sprained right knee. ... Indians RHP Danny Salazar's 48 strikeouts in 33 innings are the most by an Indians pitcher in his first five starts of a season since Sam McDowell had 49 strikeouts in 36 1/3 innings in his first five starts in 1968.