WEST HAVEN — It was simple for Tyler Cole. Every game he’d played in goal for Amity in his senior season, he’d approached it like a playoff game.

What was one more?

Cole made 37 saves Tuesday, 14 of them in the third period as Cheshire pressed for a tying goal. Jamie Blum scored two third-period goals to give the Spartans breathing room. They beat Cheshire 4-1 at Bennett Rink in the first round of the CIAC Division II boys hockey playoffs.

“We wanted home ice for the playoffs,” Cole said. “It feels great to win in front of our fans, in front of our families, and move on to the second round.”

Amity (13-8-1), the seventh seed, advances to Friday’s quarterfinal at a site and time to be announced. The Spartans will face second-seeded Watertown/Pomperaug in the quarterfinals.

Watertown/Pomperaug beat Amity 6-1 on Feb. 24.

The Spartans hadn’t won a CIAC playoff game since 2014, when they made the final before falling to Hand.

They led 2-0 after two but started the third facing the last four minutes of a major penalty for a hit from behind. Ben O’Connor scored the only goal for 10th-seeded Cheshire (9-10-2) on that power play, but that was all the Rams got.

“When we got that five-minute power play, we thought we’ve got to score two or three goals,” Cheshire coach Anthony Giusto said.

Blum’s first goal made it 3-1, but again the Spartans had to kill a penalty late. Cole made some big saves and somehow kept the Rams from popping in a long scramble around his cage.

“It’s just one of those things where, if you can’t see it, you’ve just got to have that trust in your team,” Cole said. “When it gets late in the game, it’s all them.”

Jake Silliman cleared the puck at the end of that last kill, and Blum chased it down to score the empty-netter that sealed it.

Connor Bath scored going to the net on a rebound 5:57 into the game. Jason Csejka made it 2-0 off a rebound 32 seconds into the second period, but goalie Nick Maringola kept it close for Cheshire, making 14 saves in the second.

Amity senior goalie Tyler Cole was huge in net with 37 saves.

Jamie Blum scored twice in the third period, with some second effort making the goals happen. He also had an assist.

Jake Silliman blocked shots and had a couple of key clears on the penalty kill.

The teams tied at 4 here on Jan. 31. Blum had three points in that one, too, including the late tying goal.

“(The Rams) are a great team,” said Mike Richetelli, in his first year as Amity’s head coach. “Giust does a great job with them. When we played the first time, at the end, he said, “’we’re going to do this again, aren’t we?’”

They did, and it was hard-working, physical hockey.

“It’s frustrating from a coaching standpoint,” Giusto said. “We did a lot of good things, but the season is over.”

“Today was all about hard work. We preached all week it’d be about who wanted it more, and our guys wanted it more today. They won battles on the wall. They won loose pucks.” —Richetelli