Even on an afternoon in which they faced one of MLB’s filthiest flamethrowers, the Yankees had their chances.

They made Cincinnati Reds ace Chase Burns feel the heat throughout his five innings Sunday, totaling eight baserunners and stealing six bases against the 23-year-old phenom.

They put plenty of pressure on the Reds’ bullpen once Burns departed, too.

But the big hit eluded the Yankees during Sunday’s 4-1 defeat in the Bronx, continuing a weekend-long trend while clinching a series loss to Cincinnati.

The Yankees went 0-for-9 with runners in scoring position on Sunday and left eight men on base.

They finished the series 2-for-31 with runners in scoring position — a three-game set that included an 0-for-13 performance in Saturday’s 10-2 loss.

Going back to the eighth inning of Friday night’s 5-0 win, the Yankees are 0-for-their-last-24 with runners in scoring position.

The Yankees knew they had their work cut out for them against Burns, a presumptive All-Star in his second MLB season.

But while Burns’ bread-and-butter fastball averaged 97.1 mph and maxed out at 98.8 mph, the Yankees managed to make him work.

They strung five hits and three walks against the right-hander, and in four of his five innings, the Yankees had at least one baserunner get into scoring position.

But in each of those innings, Burns stranded those runners at second or third.

Jazz Chisholm Jr. popped out with runners at second and third to end the bottom of the first.

Austin Wells popped out to leave a runner at third base to end the third — a result that left an animated Burns clapping as soon as the ball left the bat.

And in the fifth, with two outs and a runner on second, Burns struck out Cody Bellinger on three pitches, all swinging, including back-to-back 97.9-mph fastballs to finish off the at-bat.

The Yankees went 0-for-8 with runners in scoring position against Burns, who struck out seven and allowed one run over his five innings. He improved to 9-1 with a 2.00 ERA through 15 starts.

The only offense against Burns came in the third inning, when Ben Rice — after fouling off three sliders and a changeup — drilled a high, 0-2 fastball into the right-field stands.

Rice’s 22nd home run of the season gave the Yankees a 1-0 lead, but it didn’t last long.

Yankees starter Elmer Rodríguez surrendered a two-out, three-run home run to catcher Tyler Stephenson in the top of the fourth, putting the Reds up, 3-1.

Rodríguez, the Yankees’ top pitching prospect, allowed three runs over 4+ innings with two walks and a career-high four strikeouts in his fourth MLB start.

Gerrit Cole was originally lined up to start Sunday, but the Yankees decided to push their ace — and the entire staff — back by a day amid a stretch of 16 consecutive games without an off-day. Cole is now scheduled to start Monday in Detroit.

Rodríguez, whom the Yankees called up from Triple-A Scranton/Wilkes-Barre before Sunday’s game, is now 0-2 with a 4.76 ERA in the majors.

The Yankees offense had another prime opportunity to break through in the sixth inning, when righty-swinging pinch-hitter Paul Goldschmidt came up against left-handed Reds reliever Sam Moll with runners at the corners and two outs.

But the red-hot Goldschmidt flew out lazily to right field on a first-pitch sweeper from Moll, preserving Cincinnati’s two-run lead.

The Reds added an insurance run in the ninth inning when Spencer Steer snuck a slow-rolling grounder under the glove of the second baseman Chisholm and into center field.

The ball continued to slow as it reached the outfield grass, and by the time center fielder José Caballero managed to get to it and throw toward second, Steer slid in safely with a double. Caballero air-mailed his throw, and it went all the way to the backstop because catcher Ali Sanchez was out of position.

That allowed Steer to move to third, and he later scored on a Noelvi Marte ground-rule double that right fielder Jasson Dominguez couldn’t get to.

The loss capped a 3-3 homestand for the Yankees.