PHILADELPHIA — Virginia found a way to announce its return to Memorial Day weekend that was both thoroughly fitting and a break with the program’s recent history.

Appropriate because the Cavaliers led just twice until Ian Laviano’s double-overtime game-winner on Saturday.

A drastic change of pace since their 13-12 victory came against conference rival and all-around nemesis Duke, a team that effectively owned the deed to Virginia’s program for nearly a decade and a half.

No longer.

Instead, it was the third-seeded Cavaliers (16-3) moving along to Monday’s title game to face defending champion Yale, rallying from a four-goal deficit in the second half and scoring twice in the final minute of regulation to reach the final for the first time since 2011.

“I wish we could make it easier on ourselves and play well all four quarters, but the tenacity and the grit of this team is unparalleled,” senior midfielder Ryan Conrad said. “I’m so happy I get another two days with this team.”

Laviano scored four goals and Dox Aitken added three for Virginia, which got 19 saves from goalie Alex Rode. Petey LaSalla won 18 of 30 faceoffs for the Cavaliers, including the game’s final eight.

Brad Smith scored three goals for the second-seeded Blue Devils (13-5), which won a pair of one-goal games to reach championship weekend but couldn’t fend off a Virginia team that improved to 5-0 in overtime this season.

“They’ve been doing this to people all year,” Duke coach John Danowski said. “They don’t give up. They play with great skill and great confidence and poise to the end. They beat us. They clearly beat us.”

Virginia saved its best — as usual — for down the stretch. The Cavaliers got goals from Michael Kraus and Laviano in the final 45.9 seconds to force the game into overtime.

After Rode made two stops in the first extra period, Matt Moore zipped a pass from near the crease to the middle of the field to Laviano, who redirected it into the net past Duke’s Turner Uppgren.

“I’m not thinking,” Laviano said. “That’s something that me and Matt have connected on before. Incredible look by Matt, and I just had to do the easiest part and put it in the back of the net.”

It set off the latest massive celebration for the Cavaliers, who had rallied from four goals down with less than four minutes to go in regulation just a week earlier before edging Maryland in the quarterfinals.

That was a renewal of a longtime rivalry briefly cast aside by conference realignment, though the Terrapins will face Virginia in next year’s regular season. This was something else entirely, the Cavaliers being forced to navigate a program that repeatedly got the best of them, often in lopsided fashion.

Duke had won 11 consecutive meetings dating back to the 2010 NCAA semifinals, and had claimed 19 of the schools’ 20 encounters since 2005. That streak, simultaneously impressive and a bit befuddling, came to an end at the right time for the Cavaliers.

“They’ve had our number since we’ve all been here, and we knew that that was a ‘monkey on our back’ for a while,” Aitken said. “But we really this week tried to separate the history from this game, because it was the biggest stage that we’ve been on, and we really just focused on ourselves this week. We didn’t think about the 800-pound gorilla, or whatever it’s called. We just stuck to our game plan.”

Eventually, they did. Virginia was exceptionally sloppy early on, committing 13 turnovers in the first half. But Duke wasn’t much sharper, and took a 5-2 lead into the break.

It turned out to be a missed opportunity for the Blue Devils to stretch things out against a Virginia team that was once a Memorial Day weekend mainstay but was making its first trip to this stage in eight years.

“I was probably more animated at halftime than normal with this team about sort of emotional things, and this team responded,” Virginia coach Lars Tiffany said. “I said ‘Fellas this is our moment. We’ve earned this moment. We don’t deserve this. We’ve earned this. Take the moment.’”

The Cavaliers were livelier in the second half, and certainly crisper. But Duke didn’t surrender the lead easily. When Virginia closed within 8-7 at the end of the third quarter, the Blue Devils got goals from Brian Smyth and Kevin Quigley to create some breathing room. Later, they managed a four-minute possession brilliantly, capping it with a Quigley goal with 1:56 left to make it 12-10.

But the Blue Devils were never entirely comfortable, and in that sense it was in character with a team unlike so many Danowski has coached in Durham. This was Duke’s 10th semifinal trip in the last 13 years, including its second in a row, but it was probably one of the tighter Blue Devil teams to reach this stage.

That — coupled with running into hot goalies — had tripped up Duke a few times earlier in the season, and it did so again Saturday.

“We went offsides in the fourth quarter, we couldn’t win a faceoff in the fourth quarter,” Danowski said. “All the things we did for three quarters [we didn’t at the end]. Sometimes you tip your cap to your opponent and you say they made you do those things, and I get that. When we look at it from our perspective, these are some plays we would hope we would make at this time of year, but we just didn’t.”

Rather than play for a chance to bookend the decade with national titles — Duke also took Memorial Day victory laps in 2010, 2013 and 2014 — the Blue Devils instead tripped up a game shy of last year’s runner-up showing. They could bemoan their shooting (12 of 48) or their inability to deal with Virginia’s second-half invert.

Either way, it was an earlier exit than Duke envisioned for itself.

“We worked so hard after last year and losing the championship to get back,” defenseman Cade Van Raaphorst said. “To fall short, it hurts. More than anything, it’s saying goodbye to this group of guys and this program.”

Virginia delayed its farewells for another 48 hours. Now, its mainstays have played on a big stage, with an announced crowd of 32,612 on hand. And it must contend with the defending national champions, a team that jumped on Penn State with a 10-goal first quarter and never trailed in a 21-17 triumph in the second semifinal.

The Cavaliers have played with fire all spring, yet have found ways to rally time after time. Tiffany, who professed no comfort with playing from behind despite his team’s exploits, knows it would be wise not to spot an opponent a substantial lead on the final day of the season.

“There’s something to [the idea of] if you’ve never been in the moment before, can you block out the 30- 35,000 fans, and 35,000 empty seats staring at you, and it’s hard,” Tiffany said. “We felt that early at Hofstra [against Maryland], and we felt that early again today. …

“I’m no seasoned veteran, but having that experience helped me this week. Now we’re just going to, whether it’s founded or not, tell them, ‘All right, you’ve been here before, you’ve played a game here, now you’re all veterans of this.’”

Perhaps not as much as Yale, of course. But possibly enough for a team with seemingly a decade’s worth of rallies to its name to feel comfortable in a national championship game. Virginia has already heralded its return to the sport’s elite. But after exorcizing its Duke demons Saturday, there’s only one step left for the Cavaliers to finish their biggest comeback yet under Tiffany.