This would be one juicy battle of coaches if John Tortorella’s top-seeded Rangers survive the seventh-seeded Capitals after barely knocking off the eighth-seeded Senators.

If it happens, don’t expect Devils coach Pete DeBoer to “shut up” just because Tortorella told him to.

They’re such contrasts. Tortorella is a coach of fire, a la Mike Keenan or Michel Bergeron; DeBoer one whose benchwork more resembles Al Arbour or Roger Neilson.

That’s why it was such a hoot when DeBoer went off on Tortorella’s screamed objections to the Devils’ starting lineup March 19 at Madison Square Garden. Three fights in three seconds was the escalation of two prior Anthem Antics this season, including the initial one, when Tortorella first designated his punchers as the starters in Newark.

“Either he has short-term memory loss or he’s a hypocrite. It’s one or the other,” DeBoer declared.

The next day, Tortorella told DeBoer to shut up, and suggested that he, Tortorella, should follow his own advice.

NHL VP Colin Campbell, in charge of disciplining such situations, strongly delivered his negative views on the spectacle to both DeBoer and general manager Lou Lamoriello.

A playoff game is an unlikely spot for more Anthem Antics, but the coaches are probably not planning vacations together.

Tortorella made his name by winning one Stanley Cup for Tampa Bay while DeBoer failed to make the playoffs in three years in Florida.

DeBoer’s unimpressive pro resume makes Lamoriello look good now in hiring him over favorite Michel Therrien, told the morning of DeBoer’s press conference that he wasn’t getting the Devils job.

DeBoer has gone one round deeper than Lamoriello did, ending the Devils’ nine-year failure to reach the semifinals, surpassing Brent Sutter of 2008 and 2009, Jacques Lemaire of 2010, and yes, Lamoriello of 2006 and 2007.

From the start, DeBoer has been a student of his team, almost in equal parts as its teacher and taskmaster. Mostly, his players say, he relies on rationality and reason, rather than high-volume rants.

DeBoer and his players credit the assistants, Dave Barr, Adam Oates, Larry Robinson and Chris Terreri, in large part, with keeping communication open.

But it’s the coach’s style that defines the team, and DeBoer does not make his decisions irrevocable, or matters of dogma. Nearly every time an on-ice performance issue has needed addressing, he does so promptly.

The exception was when Adam Larsson had long become costly but DeBoer admirably stuck with the prize rookie. When complete meltdown loomed, DeBoer mercifully pulled the plug, and now Larsson is back in the lineup, although for how long is uncertain.

Ilya Kovalchuk came into camp saying “enough experimenting” about playing right wing, yet DeBoer was able to convince Kovalchuk to buy in.

It appears DeBoer explains his thinking, something many coaches don’t do, and players are more receptive when they understand reasons. The players say games are dissected in an impassive manner, where error, but not blame, is noted. DeBoer deals with his players in a natural and honest fashion, without head games, and they appreciate it.

Coaches usually get the benefit of doubt from their players in their first year together. The Devils may be getting the benefit of that now.

* The status of defenseman Marek Zidlicky is uncertain, called “day-to-day” after he was knocked out of series finale Tuesday in Philadelphia. Zidlicky was knocked into the boards, face-first, by a forearm to the head from Wayne Simmonds. … Individual game tickets for the Eastern Conference finals will go on sale to the general public today at 11 a.m.