The Miami Marlins, still hoping to pull off a late run over the final three weeks of the regular season and end their 13-year playoff drought, nearly made headlines for all the wrong reasons on Saturday night.

Until Jeff Francoeur singled off the glove of Dodgers shortstop Corey Seager with two outs in the eighth inning, the Marlins were only four outs from becoming the first team in baseball history to be on the losing end of a combined perfect game.

But Francoeur’s line drive off reliever Joe Blanton in the eighth denied the Dodgers — who own 25 no-hitters in their history, more than any other team — a no-no and a perfecto.

Los Angeles settled for a two-hit, 5-0 shutout of the Marlins in front of 20,933 fans at Marlins Park.

With their 13th loss in their past 18 games, Miami (70-72) fell  5 1/2 games back of the St. Louis Cardinals for the second and final wild-card spot in the National League with only 20 games left.

“It’s one of those things where you run kind of into a buzzsaw,” said Francoeur, who was shocked to see the Dodgers pull starter Rich Hill after seven perfect innings.

“He’s got that curveball working like that, it’s tough, and we just weren’t able to make the adjustments. [Marlins starter] Tom [Koehler] kept it close for a while. But we just didn’t give him anything to work with. In 11 years in the big leagues I’ve never had a no-hitter or a perfect game against my team. I was praying to God this wasn’t the first one. I’m glad we were able to come through with a few hits.”

Hill, a 36-year-old soft-tossing left-hander, retired the first 21 Marlins he faced on only 89 pitches, striking out nine. But with a history of blister problems and Los Angeles comfortably in front, Dodgers manager Dave Roberts turned to his bullpen to pitch the final two innings.

Hill said the blister that put him on the disabled list for more than a month wasn’t bothering him at all. He wasn’t happy to come out of the game but understood why Roberts made his decision with the Dodgers in a contending situation.

“I feel sick to my stomach,” Roberts said. “Rich had an opportunity of a lifetime. [But] you take the personal aside. It’s the toughest thing I’ve had to do. But I know it was to give us the best chance to win a World Series.”

Los Angeles (80-61) got all the offense it needed on four home runs to right field.

Joc Pederson hit two of them. He ended Koehler’s run of 10 consecutive scoreless innings and put the Dodgers ahead 1-0 when he blasted a solo shot into the upper deck in right field with two outs in the fifth.

An inning later, Los Angeles knocked Koehler out of the game after Seager belted a two-run homer into the seats in right and Justin Turner followed with another long blast right after Seager’s.

But the story was Hill, who was making his third start for Los Angeles and still hasn’t given up an earned run in 19 innings for the Dodgers. Acquired from the Oakland Athletics in a five-player trade on Aug. 1, Hill has gone 9-0 in his past 11 starts with a 1.43 ERA since May 7.

Hill made his major-league debut against the Marlins as a reliever for the Cubs on June 15, 2005, and he got beat up, giving up two runs on three hits in an inning.

Before Saturday night, he had not pitched against the Marlins since June 25, 2009, when he was with the Baltimore Orioles. That night, the Marlins tagged him for six runs on eight hits in  4 1/3 innings in an 11-3 victory.

But he was on his game from the start on Saturday night, using his 73- and 74-mile-per-hour curveballs and occasional 90-to-92-mile-per-hour fastballs to keep the Marlins off balance. He struck out four of the first nine batters he faced and then whiffed five in a row between the fifth and sixth innings.

Left fielder Yasiel Puig preserved Hill’s perfect game when he robbed Martin Prado of an extra-base hit with a diving catch on the warning track for the final out of the seventh. It was the hardest hit ball of the night off Hill.

Said Hill: “Obviously, I didn’t want to come out of the game. But I think there is a bigger picture here, and we all know what it is.”

Hill, who has played for eight major-league teams in his 12-year career, mostly as a reliever, and who before this season was 26-23 with a 4.54 career ERA, improved to 12-3 with a 1.80 ERA this season.

“I’ve come up through the minor leagues with Rich,” Francoeur said. “He was a big-time prospect. He’s always had the stuff. I think he ran into some arm problems and then just could never stay healthy and then find it. You’ve seen him the last two years really turn his career around. He’s a big-time pitcher. He showed it tonight.”

Had Hill remained in the game, there’s no telling if he would have completed only the second perfect game in Dodgers history or not.

After Francoeur’s two-out single in the eighth ended a string of 23 consecutive outs, Adeiny Hechavarria reached base against Grant Dayton to open the ninth when he hit a hard ground ball to third that resulted in a throwing error by Turner. One out later, Dee Gordon reached on an infield single to third. But the Dodgers got out of the inning unscathed.

It was the 11th time this season the Marlins have been shut out.