NEW YORK -- They don’t play the games on paper, as the saying goes. But if they did, this would’ve been a series you’d pencil in as a win for the home team -- the mighty Yankees, owners of baseball’s best record, going up against a last-place Reds club that might shop their best pitcher to a postseason contender within weeks.

Instead, when DJ LeMahieu’s flyout dropped into center fielder Nick Senzel's glove in the 10th inning on Thursday, the Yankees had absorbed their fourth series loss of the season. New York’s comeback fell short, its late bullpen struggles too much to overcome in a 7-6 loss to Cincinnati at Yankee Stadium.

“Tough losses, but we fought back always,” said Aaron Judge, who hit his Major League-leading 31st homer in the defeat. “I wish we could have scored a little bit more runs early, especially tonight, but they’ve got a good ballclub over there and they battled. Their record may show something different, but they’ve got a lot of good ballplayers over there.”

How unexpected was the Reds' upset? According to STATS, it marked just the sixth time in Major League history that a sub-.400 team won a road series against a club with a .700-or-better winning percentage (minimum 50 games into a season). It hadn't happened since 2001, when the Royals outplayed the Mariners. Before that, you'd have to go back to a 1955 Pirates-Dodgers series.

The Yanks pace the Majors in comeback wins (27) and walk-off wins (11), but they couldn’t add to those tallies on Thursday. Having lost four of their past five games, the Yankees were held to one run and two hits through seven innings by a dominant-as-advertised Luis Castillo.

It was a showcase that informed the Yankees -- and their rivals -- that the Bronx lights would not burn too brightly for the flame-throwing righty, who may be a prized (and pricy) acquisition ahead of the Aug. 2 Trade Deadline. Any potential deal for Castillo would likely cost the Yankees one of their top prospect shortstops: Anthony Volpe or Oswald Peraza.

• Volpe stays hot with homer on two-hit night

“He’s nasty,” Yankees manager Aaron Boone said. “Two-seam, four-seam, 95-99 [mph] that he paints to both sides of the plate. He’s giving you two different looks with the fastball, and he’s working both sides of the plate with it, then he’s got a great changeup. He was tough.”

Said Judge: “When you’ve got 100 [mph] and you’re painting the corners, it’s going to make for a tough day.”

The Yanks could use a guy like that, especially on a day when Luis Severino emerged from an MRI tube to land on the 15-day injured list with a right lat strain. Nestor Cortes did his part to help, matching Castillo nicely through seven innings of one-run ball, turning over the lineup three times on just 89 pitches.

Cortes said he made adjustments after recording just 11 outs in his last start in Boston. The All-Star left-hander was 5-1 with a 1.50 ERA and four homers allowed in his first 10 starts, but he had been 2-2 with a 5.34 ERA and nine homers allowed in the six starts before Thursday’s outing.

“Just throwing to my areas; not big adjustments, just going back to what I’d been doing for the first 12 starts,” Cortes said. “Those outings were pretty good. I watched some video, looked at some stuff and tried to be that guy again.”

With several key relievers (Clay Holmes, Michael King and Wandy Peralta) unavailable after appearing in the first two games of the series, Boone said before the game that he planned to reinsert Jonathan Loáisiga to high-leverage situations, calling the right-hander “a stud.”

Cincinnati peppered Loáisiga for four hits in a three-run eighth inning, his first appearance since missing 47 team games with right shoulder inflammation.

“Things didn’t work out the way I wanted,” Loáisiga said through an interpreter. “I was definitely trying to get ground balls there for double plays.”

New York broke through against the Reds’ bullpen, with Marwin Gonzalez’s 12-pitch walk in the seventh inning having swelled Castillo’s pitch count. Facing Jeff Hoffman in the eighth, Judge went deep, then Torres launched a two-run shot that tied the game.

But Hoffman and Hunter Strickland set the Yanks down in order in the ninth inning, sending the contest to extra frames for the second time in as many nights.

Cincinnati took a three-run lead in the 10th, with Joey Votto, Tyler Stephenson and Donovan Solano connecting for run-scoring hits off Lucas Luetge. Matt Carpenter brought the Yanks within a run with his 11th homer (in 68 at-bats), a two-run shot off Reiver Sanmartin, but LeMahieu skied to center with two men aboard for the final out.

“It’s a tough one,” Judge said. “You never want to lose a series, but sometimes you’ve got to tip your cap and get ready for the next one.”