NEW YORK -- The Yankees sensed momentum might be on their side in the eighth inning as Anthony Rizzo dashed for second base, soon to score a game-tying run. They felt confident when Michael King struck out the side in the 10th inning, and they knew for sure once Josh Donaldson lifted a fly ball to deep left field in the home half of the frame.

As they have done all season, these Yankees continue to own the Bronx. Donaldson’s sacrifice fly scored Aaron Judge with the deciding run as the Yankees celebrated their sixth walk-off win of the season, completing a perfect homestand with a 5-4 victory over the Tigers on Sunday afternoon at Yankee Stadium.

• Box score

“We want to dominate at home,” Rizzo said. “The more we dominate here, the more this city is going to buzz and the fan base is going to buzz. I know from experience, coming into New York and playing here, the lights shine brighter and the fans are into it. It’s definitely intimidating when you’re on the other side.”

For the Yankees, owners of a Major League-best 39-15 record, the win marked their sixth consecutive victorious homestand, as they swept both the Angels (3-0) and the Tigers (3-0). This is the seventh time in franchise history that the Yanks have won 39 of their first 54 games and the first since 1998, when they were 41-13.

“Some winning things happened,” manager Aaron Boone said. “Just a lot of guys with a hand in a victory again.”

Concluding a week largely fueled by dominant starting pitching, Jordan Montgomery provided a solid performance in a no-decision, but many players could claim having offered a hand. Donaldson got the final swing, choking up to barrel a Gregory Soto heater deep enough to send a crowd of 38,030 home happy.

“I think we’re just playing good baseball,” Donaldson said. “Our pitching really set the tone early for this series. We just didn’t give them much at all. Today they showed some fight like we knew that they would. We were able to scrap out runs in a couple of different ways today, which is nice to see.”

Mired in a season-long slump, Joey Gallo put New York on the board in the fifth inning, connecting for his sixth homer of the year, a two-run shot to right field off Rony García. The blast was Gallo’s first since May 15; his 1-for-3 showing raised his batting average to .176.

“Every hit is nice,” Gallo said. “It was a big home run, and we got a little momentum. It feels nice to just help the team and come through. I feel like I haven’t helped the team too much at the plate lately, so that felt good, coming into the dugout and feeling like I contributed.”

DJ LeMahieu provided the Yanks with a lead in the seventh, trotting to first base on a four-pitch free pass from Alex Lange with the bases loaded. In the eighth, Detroit briefly took the lead on run-scoring hits by Miguel Cabrera and Javier Báez -- an advantage reclaimed in the home half of the eighth as Rizzo stole second, advanced on an error and scored on Gleyber Torres’ slow tapper up the third-base line.

“I was timing [Michael] Fulmer up a little bit and I thought he was forgetting about me a little bit over there,” Rizzo said. “I was going to take a shot with one pitch and it worked out. The throw got away, too, and I was able to advance to third. Gleyber did enough to get me in. Those are things down the stretch and over the long haul that make differences.”

Added Tigers manager A.J. Hinch: “They outplayed us in the game. They out-executed us and they are a winning team. At the end of the game, it gets even more magnified when you miss some opportunities.”

Montgomery limited the Tigers to two runs and five hits over 6 1/3 innings in a no-decision. Those runs came in the fourth, on a Báez RBI double and a Daz Cameron RBI single that Torres attempted to backhand at second base.

But that was all Detroit would muster against Montgomery, who has established himself as a steady member of the tight-fisted Yankees rotation. Bombers starters have permitted only 16 runs over their last 11 games, matching their lowest total in franchise history (Aug. 20-28, 1963). Those contributions are a crucial ingredient as to why the Yankees sit atop the standings.

“It’s fun,” Montgomery said. “Everyone is going out there and throwing strikes. You just keep competing, keep us in the games. We’re just trying to keep building off each other, I guess.”