Exhausted and exhilarated after scoring the biggest goal he might ever score, a half-stunned Andrew Shaw meandered through a postgame interview on national television, casually slipping in an F-bomb.

“Slip of the tongue,” Shaw said later. “I was exhausted. I couldn’t think at all. Could barely breathe. I think I made up a word in there, too.”

No worries. It was after midnight, anyway.

Shaw tipped in Michal Rozsival’s shot from the point after Dave Bolland deflected it first with 7:52 left in the third overtime — and seconds before the clock struck midnight — as the Hawks pulled out a heart-stopping 4-3 victory over the Boston Bruins on Wednesday night in Game 1 of the Stanley Cup Final before 22,110 delirious and depleted fans at the United Center.

“Obviously emotions are high,” Shaw said. “Too exhausted right now to express it.”

Corey Crawford was spectacular in goal for the Hawks, making 29 of his 51 saves in the extra sessions in a career-defining performance, including 12 in a riveting, back-and-forth first overtime full of end-to-end rushes and golden scoring chances. Of Crawford’s effort, Hawks captain Jonathan Toews said, “You can’t even put it into words.”

Crawford had a word for it, though: Fun.

“A lot of hockey in the Final, in OT, yeah, it’s pretty fun, man,” Crawford said.

Fortunately for both teams, there are two days off until Game 2 on Saturday night.

“It’s just part of the playoffs,” said defenseman Duncan Keith, who played a team-high 48 minutes, 40 seconds and had to sit down briefly before cutting a postgame interview session short, understandably drained from the marathon game. “You have to battle through things like that. There’s no saying you’re tired. It’s just finding a way.”

In just one magical, marathon game, this Stanley Cup Final lived up to the hype — an Original Six matchup between the league’s best two teams, each balanced with skill and speed, physicality and fortitude, defense and goaltending.

It didn’t take long for the Hawks to realize the Boston Bruins are not the Kings, easily beaten with skill and speed, helpless to score. And it didn’t take long for the Bruins to realize the Hawks are not the Penguins, easily stifled and easily frustrated. It just took really, really, really long to decide a winner.

The resilient Hawks rallied from a two-goal deficit on goals by Bolland and Johnny Oduya against the team perhaps best suited to protect a lead in the league — scoring as many goals in a 4:14 span of the third period as Pittsburgh did in Boston’s four-game sweep in the Eastern Conference final — to send the game to overtime.

But that was only the beginning.

The first overtime was simply breathtaking, full of surprisingly wide-open, end-to-end action, with Crawford saving the game a half-dozen times in the face of wave after wave of Bruins chances — including one of two too-many-men penalties the Hawks had to kill in overtime — with the Hawks counterpunching just enough to keep things impossibly tense.

The pace slowed down in the second overtime as fatigue set in, but there were still gasp-inducing moments, including Crawford stopping Tyler Seguin twice, Torey Krug on a big rebound, and catching a break with 12 seconds left as Zdeno Chara’s power play shot ticked off Milan Lucic’s stick and hit the post, sending the game to a third OT.

Crawford continued to make spectacular stops in the third overtime, keeping the Bruins at bay just long enough for the Hawks to pull out the win. Rozsival’s shot from the point was tipped first by Bolland, then by Shaw for the game-winner, turning a still-full United Center into a late-night party.

Once again, it was the Hawks’ third- and fourth-liners producing the goals.

“They’ve been great all playoffs,” Keith said. “It’s tight checking. Those guys — Toews and those type of guys — they’re playing against [Boston’s] top ‘D’. There’s not a lot of space. The checking guys, guys like Shaw and [Bryan] Bickell, those guys have been great for us all year and all playoffs.”

The Hawks finished with 63 shots on goal, 40 shot attempts blocked, and 29 shots missed.

Lost in the unlikely finish was the unlikely way it got there, with the Hawks rallying from two two-goal deficits to force overtime in the first place.

Lucic scored at 13:11 of the first period on a prototypical Bruins goal. David Krejci’s forecheck behind the Hawks goal allowed him to get the puck to Nathan Horton — Niklas Hjalmarsson went for the hit on Krejci instead of the puck, and it cost him — and Horton chipped it to Lucic, all alone in the slot, for the bang-bang goal. That gave the Bruins a 1-0 lead, and quieted the crowd.

Lucic scored again just 51 seconds into the second period, triggering the play himself by winning the battle along the boards, then drilled a one-timer from Krejci off Oduya’s stick and past Crawford for a 2-0 lead.

The Hawks — with coach Joel Quenneville firing up the line blender with gusto — came roaring back after that.

Brandon Saad, held without a goal all postseason, finally got on the board, reunited with his old linemates of Hossa and Jonathan Toews, at 3:08 of the second. Hossa did the dirty work, stealing the puck in the corner and feeding Saad for a sharp one-timer, cutting the Hawks’ deficit to 2-1.

“It was huge for him and huge for our team,” Toews said. “That was a timely goal and I think we needed something to get our crowd into it, give us energy on the bench. Great shot by him. I think as a line with Hoss and Saader and myself, we created quite a bit of offense tonight.”

After the Hawks squandered three power plays — including a 5-on-3 — Boston got a power play goal by Patrice Bergeron to take a 3-1 lead early in the third.

But the Hawks responded with two goals from unlikely sources. Less than two minutes after Bergeron scored, Bolland scored his first of the playoffs, one-timing an Andrew Shaw feed. Four minutes later, Oduya’s shot from the point was headed well wide of the net, but hit Ference’s skate and bounced past a stunned Rask to tie the game at 3-3 with 7:46 to go in the third period, sending the game to overtime and setting the stage for a long, unforgettable night at the United Center.

“It’s fun being in the finals, the last two teams playing, all the hockey world is watching,” Hawks winger Patrick Sharp said. “And to [get] an effort like that from both sides, it was fun to be a part of. And thank God it’s over.”