Even though it took a few extra minutes on Saturday, the Islanders earned yet another victory at home.

Anthony Beauvillier scored in overtime to lift the Islanders to a 3-2 win over the Sabres, extending their home winning streak to six games and snapping the Sabres’ win streak at three.

Beauvillier scored on a breakaway at 3:04 against Sabres goalie Linus Ullmark for his 10th goal of the season. He finished off a sequence in overtime in which he accidentally got tangled up with Ullmark in the crease, then was tripped in the Sabres zone before he corralled the puck for the winning play at Nassau Coliseum.

“I put my head down, put a shot on goal and it went in,’’ he said of his extra-session score. “I found some legs on the way to the breakaway. I’ll take it.”

The Islanders improved to 13-2-1 overall between the Coliseum and Barclays Center this season.

“We got the win, the two points,’’ Islanders coach Barry Trotz said. “That was paramount.”

Semyon Varlamov made 33 saves for the victory to improve to 11-3-2 on the season, his first with the Islanders.

“Varly was solid,’’ Trotz added. “When he had to make a save, he did.”

Jordan Eberle had snapped a 1-1 tie with a goal early in the third period to give the Islanders a 2-1 lead, but Sabres captain Jack Eichel tied it with a power-play goal at 18:14 after the Sabres pulled Ullmark for an extra skater while Islanders forward Mathew Barzal served a roughing penalty.

Eichel’s 23rd goal of the season was assisted by Rasmus Ristolainen and Victor Olofsson and sent the game into overtime. Eichel has extended his points streak to 16 games when he assisted on Victor Olofsson’s second-period goal. Eichel has 15 goals and 14 assists during the streak.

Sabres coach Ralph Krueger was upbeat despite the defeat.

“It was an outstanding hockey game, hard fought to the last second,’’ he said. “They played their game and I was proud we played our game. I thought there were a lot of times we dominated but didn’t create scoring chances. Disappointing in overtime but generally a super effort by the guys.”

Eberle, who entered the game with only two goals in 20 games this season, scored his third at 4:50 of the third when his shot from the slot eluded Ullmark. Brock Nelson assisted.

Eberle signed a five-year, $27.5 million free-agent contract in July to stay with the Islanders after scoring 19 goals last season and 25 the previous one for the Islanders.

Michael Dal Colle opened the scoring for the Islanders at 5:11 of the first period when he knocked a loose puck past Ullmark. Beauvillier had the lone assist.

The goal was the second this season for Dal Colle, the fifth overall pick by the Islanders in the 2014 draft who found a spot in recent games on a line with Beauvillier and Nelson. Dal Colle later left the game with an upper body injury thus Eberle became part of the unit in the third.

“Guys that fill in are excited to jump on that line,’’ Trotz said.

Olofsson had tied the game with a power-play goal at 6:11 of the second, rifling the puck past Varmalov. The goal was Olofsson’s 14th this season, which leads all rookies. Assists went to defenseman Rasmus Dahlin and Eichel.

Olofsson has 21 points in the past 19 games — with eight goals and 13 assists. The 24-year-old Swede was a seventh-round pick by the Sabres in 2014, taken 176 spots after Dal Colle. Olofsson also leads NHL rookies with 31 points overall.

The Islanders were returning after a three-game road trip on which they won at Tampa Bay and Florida after a loss in Dallas.

They have won eight straight games at Nassau Coliseum during a season in which they are splitting games between Long Island and Brooklyn, playing 28 contests at Nassau Coliseum and 13 games at Barclays Center.

Despite Buffalo’s late tying goal, Beauvillier said there no panic on the Islanders bench.

“As soon as the third period was over, we just said let’s go get the two points,’’ added the 22-year-old Beauvilier, who has 20 points this season. “They scored late but we did a good job coming back and staying focused.”

Buffalo arrived on an offensive surge with 36 goals in its past nine games during which it was 5-1-3. The Sabres met the Islanders and their stingy defense, which has permitted a league-low 72 goals over the first 31 games.