Two years ago on May 1, Jameson Taillon walked off the mound in Texas with a win but an injured elbow, staring down a second Tommy John surgery.

Saturday, the healthy Yankees right-hander recorded his first win since.

Taillon struck out eight and gave up just one run over five strong innings to lead the Yankees to a 6-4 win over the Tigers at Yankee Stadium.

“It took me a little longer than I would have liked to get that first win here, so that makes it meaningful to get on the board and get it out of the way,” Taillon said with a chuckle after his fifth start in pinstripes.

“There were times where I wasn’t 100 percent sure whether I’d be back in a big league uniform, let alone to be on a team like the Yankees and contribute to wins throughout the year. Now I’m just looking forward to putting my head down and knocking out more starts.”

Taillon continued a string of strong starts from the rotation. His outing marked the 12th time in the past 13 games that the Yankees starter has allowed three runs or fewer, with the club 8-5 in that stretch.

Saturday wasn’t the laugher the Yankees (13-14) breezed to Friday night in a 10-0 win, but with Aaron Judge and Gleyber Torres combining for five hits and six RBIs, they continued to inch back toward .500 — within one game of it for the first time since they were 5-6.

“[Taillon] was player of the game for us today,” Judge said. “It was a special moment. … He’s a guy that, through all of it, has stayed positive and continued to work, work, work. It’s really showing right now. I know it’s only been a couple games with us, but I’m excited to see what he does the rest of this year with us and beyond.”

Taillon had held the Tigers (8-20) hitless through three innings before giving up his only run of the day in the fourth inning on a solo home run by Jeimer Candelario, tying the game at one.

In the fifth inning, Taillon faced his biggest test after issuing a pair of walks to load the bases with two outs for Miguel Cabrera. But Taillon remained composed and struck out Cabrera with a 94 mph fastball at the top of the zone — a combination he thrived with all day — to escape the jam.

“That made that moment that much bigger to be able to get him there, because he’s come up big in a lot of spots over the years,” Taillon said of Cabrera.

Judge then ensured Taillon would leave in line for the win in the bottom of the fifth, crushing a double to score DJ LeMahieu for the 2-1 lead.

An inning later, Judge and Torres each added a two-run single to put the Yankees up 6-1 and give them some breathing room the rest of the way. The Yankees wound up needing it after Justin Wilson and Chad Green combined to give up three runs before Aroldis Chapman slammed the door shut in the ninth for his fifth save in five chances this season.

In his first four starts of the year, Taillon had struggled to put batters away with two strikes. Opponents entered the day batting .288 off Taillon with two strikes, but he held the Tigers 0-for-11 with two walks in those scenarios on Saturday.

“I thought my awareness to the situation was a little better. I slowed it down and I was aware that, ‘Hey, this is one of the situations where I need to make a pitch.’ ”

Taillon delivered them to preserve his milestone win.

“To get back to this point, contributing to this team, really happy for him today,” manager Aaron Boone said. “It was another really good step forward for him.”