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MIAMI — The only time Cardinals righthander Dakota Hudson had finished the seventh inning in the major leagues was last year, when he was a rookie reliever. But in his previous five starts this season, he had knocked on the door of the seventh — lasting 6, 6, 6 1/3, 6 and 6 1/3 innings, in order.

Finally, he pushed it open Tuesday night when he fanned Miami’s Curtis Granderson to strand a runner at first to end the seventh in another stellar start.

“‘Waino’ (teammate Adam Wainwright) always says, ‘If you want to win baseball games, you’d better go seven,” said Hudson, smiling. “I finally hit that bench mark so I’ll have to give him a call later.”

Hudson, for the third consecutive outing, allowed only one run. He has given up five or fewer hits (four on Tuesday) in all of them. And the Cardinals won for the fifth consecutive time in a Hudson start as they belted the Miami Marlins 7-1 with a 13-hit attack before 6,308 paid customers at Marlins Park. That was even fewer than straggled in out of the heat on Monday.

“I feel like every time I take the ball, our team is ready to win,” Hudson said.

The Cardinals certainly always knock the Marlins around here. Their 62-35 record (.639) in Miami is the best of any team against them since the Marlins joined the National League in 1993

It marked the third time this season that the Cardinals had back-to-back quality starts on the road, with Hudson (5-3) a part of all three. The 24-year-old who won a starting job in spring training after strictly relieving last year has had six consecutive quality starts (three earned runs or fewer over at least six innings).

“You see why we did what we did in spring training,” Cardinals pitching coach Mike Maddux said.

Manager Mike Shildt added, “He’s got great stuff and great demeanor and great preparation. His tempo was good. A lot of positives tonight.”

Now that Hudson has reached seven, the next logical goal would seem to be eight innings. But he said “I’m pushing for nine every time out there.”

• BOX SCORE: Cardinals 7, Marlins 1

Because Hudson had thrown just 93 pitches after seven, Shildt said Hudson probably could have gone longer Tuesday.

“We got into a situation where they didn’t want me to strike out again,” said Hudson, who whiffed three times, including once with the bases loaded.

Hudson was quick to appreciate his defense, notably Marcell Ozuna making a catch to save a run or two in the fourth inning. Third baseman Yairo Munoz made two strong plays back to back in the sixth and Paul Goldschmidt started a tricky 3-6-3 double play.

Cardinals catchers Matt Wieters and Andrew Knizner had been nothing for 27 (20 of those by Wieters) in the past 10 days with Yadier Molina on the injured list. But Molina, his right thumb tendon healed, came off the IL on Tuesday and had two hits, including a leadoff double in the eighth as the Cardinals put the game away with three runs.

The two hits were one thing but Shildt said that Molina “has just got the presence that makes people around him better. There’s tangible and intangible and all of them are superior across the board.”

After Molina’s double, Kolten Wong bunted for a hit and Dexter Fowler, who had been five for 45, slashed a run-scoring single for his first of his two hits. Pinch-hitter Jose Martinez, batting with men at first and second, singled to right center and Fowler followed Wong home, scoring all the way from first when right fielder Harold Ramirez returned the ball to second base and third-base coach “Pop” Warner changed his mind and waved Fowler home.

“I think I can score on anything,” Fowler said. “I had to stop, but I was running on the pitch so I figured I was going to score anyway. I looked up and the ball was going to second and I was already rounding third.”

Fowler, who had slipped under .240, hit another ball hard to deep right.

“The (recent) rain delays and off days kind of get you out of your rhythm a little bit,” he said. “But I’ve got to roll with the punches. That’s part of it.”

Goldschmidt narrowly missed what would have been his 13th homer when his one-out drive to left in the Cardinals’ sixth inning hit the padding atop the wall and he had to settle for a double. But Goldschmidt would score the go-ahead run on an error by Miami shortstop Miguel Rojas as the Cardinals took a 3-1 lead over in an unusual inning.

After Goldschmidt’s double, only his sixth of the season, Ozuna legged out an infield hit behind second, with Goldschmidt stopping at third. Molina then lined to the left of Rojas, who made a diving catch for the out then threw to first to try to get Ozuna. The throw was wild, enabling Ozuna to get back safely. The ball rebounded to first baseman Garrett Cooper, who fired home to try to get the sliding Goldschmidt — who alertly had tagged and then come home. Goldschmidt barely arrived safely with a good slide.

Ozuna and Wong, who had walked, executed a double steal but Fowler contested he was hit by a pitch.

“The ball doesn’t lie,” Fowler said.

But the replay officials didn’t see it the same way and Fowler’s at-bat continued as the Cardinals lost their challenge. Fowler wound up walking, as did Harrison Bader, who drove in his second run with his bases-loaded walk.

Ozuna hit his 18th homer, in the ninth inning.

The Cardinals, who had dipped below .500, have nudged themselves back over it. Their starting pitching was stout, their defense crisp and their base running free-wheeling.

“Just play the game the right way,” Wong said. “Play it hard. Whatever happens, happens.

“We know we can play.”

Rick Hummel is a Cardinals beat writer for the St. Louis Post-Dispatch.