There is still a Boston sports team that started its season in September courting perfection, lighting up scoreboards, and making every one of its games a save-the-date occasion.

In a town that worships winners, the Boston College women’s hockey team is the ultimate can’t-lose club. BC not only has a chance to win it all, it has a chance to win them all. The No. 1-ranked Eagles finished off their regular season unblemished and unbeaten at 34-0-0, no ties for the hockey history makers at The Heights. BC became the first team — men’s or women’s — to finish unbeaten and untied in Hockey East play, going 24-0.

The Eagles (36-0-0) advanced to the Hockey East semifinals Saturday night with a 5-1 victory over Maine, giving them 10 goals in the two-game sweep.

Recognition equality seems to be eluding a team that has been unequaled this season. It’s time to take notice because this type of sustained excellence is rare and special in sports. It’s one of the reasons we watch sports.

This is UConn women’s basketball-type sublime supremacy from the Ladies of the Rink. The Eagles led the nation in goals scored (185), goals per game (5.44), and average scoring margin (plus 4.26). Such a team deserves more than the 298 fans who showed up Friday in Chestnut Hill, barely drowning out their directives on the ice.

“At the beginning of the season, no one kind of knew who we were or anything,’’ said senior winger Haley Skarupa. “But you can see more people come to the games, and more people are asking about us, not even just on campus. . . . So, I think we’ve kind of made a name for ourselves this season. It’s really cool to see that we’ve earned that.’’

The formula for an all-time team is roster depth, resolve, relentlessness, and a bit of heartbreak.

The Eagles are led by incomparable senior center and cocaptain Alex Carpenter, who led the nation in scoring during the regular season (38 goals and 38 assists) and has more career points than any player — male or female — who has laced up skates for BC.

The pucks progeny of local schoolboy legend and longtime NHLer Bobby Carpenter, she is the reigning Patty Kazmaier Award winner — the women’s hockey equivalent of the Heisman Trophy.

She is part of a senior class that is laser-focused on erasing the disappointment of last season, when BC started 27-0-1 with a 25-game win streak but lost the Beanpot final, the Hockey East tournament championship game, and in the Frozen Four.

Carpenter, linemate Skarupa, and cocaptain Dana Trivigno are the senior leaders. Skarupa ended the regular season third in the nation in points with 66 and trails only Carpenter in the program’s scoring annals.

After their undefeated spell last year, the Eagles are a bit ambivalent about chasing perfection and reluctant to acknowledge its presence.

The mantra preached all season by coach Katie Crowley, a gold-medal winner with the 1998 US Olympic team, has been to improve from each game and forget the record.

“We have bigger goals than what that record is,’’ said Crowley.

The biggest goal is bringing BC its first national title in women’s hockey.

The Eagles have advanced to the Frozen Four in four of the last five seasons, but have never reached the title game.

“I feel like we wouldn’t really be comfortable losing a game at this point,’’ said Skarupa. “We’re too competitive for that. But at the end of the day, a national championship, whatever it takes to get there, we’re willing to go through that.’’

Every team wants to be the first to hand BC its first loss. Boston University has come the closest, taking the Eagles to overtime Nov. 10.

A Maine team BC had dominated in the regular season, winning three games by an aggregate score of 16-2, had the Eagles in a one-goal game in the third period Friday before Trivigno scored on a gorgeous spin move.

Still, if it weren’t for the sharp goaltending of sophomore Katie Burt, who has an “Entering Lynn’’ graphic on her mask — an homage to her hometown — but doesn’t let many pucks enter her net, the game could have been a nail-biter instead of a 5-2 triumph.

It’s not just talent that has BC chasing history. (BC has three of the 10 finalists for the Patty Kazmaier Award this season — Carpenter, Skarupa, and sophomore defenseman Megan Keller.)

Special teams usually have a special bond.

The Eagles have a ritual on Thursday nights at Edmond’s Hall, a dormitory that is a Doug Flutie Hail Mary away from Alumni Stadium. There they gather to indulge in ABC’s lineup of Shonda Rhimes shows: “Grey’s Anatomy,’’ “Scandal,’’ and “How to Get Away with Murder.’’

Bonding over over-the-top dramas isn’t BC’s secret, but it builds morale and trust.

Fans of the 2007 Patriots can vouch for how the pressure to maintain perfection can wear down a team. But BC isn’t backing down.

Only one team in women’s hockey history has completed a perfect season. Minnesota went 41-0-0 in 2013.

“I feel like a loss would almost be like we didn’t do the best we could,’’ said Trivigno. “I mean, if we play BC hockey, and I’m sure Coach Katie and everyone else would tell you, I truly believe we have a chance to win. If we play BC hockey every game, I feel we that we should win every game. If there does happen to be a loss, then we didn’t do our best or the other team played really well. So, I mean I want all wins.’’

At least one local team could still deliver on the promise of perfection.

Christopher L. Gasper is a Globe columnist. He can be reached at cgasper@globe.com. Follow him on Twitter @cgasper.