You know that five-year contract Alain Vigneault signed to coach the Rangers in July of 2013 meant to keep him on the job through the end of next season?

Well, not any longer … or to be more precise, it is now for longer than that, with The Post learning exclusively that the Blueshirts have extended Vigneault’s contract by two years through 2019-20 with a bump on the coach’s annual $2 million income.

So no prospective lame duck behind the New York bench at the Garden on Tuesday, when the Blueshirts face the Blue Jackets and John Tortorella, Vigneault’s predecessor on Broadway. And no offseason questions about the club’s direction behind the bench.

Because Rangers president Glen Sather and general manager Jeff Gorton — in consultation and conjunction with Garden chairman Jim Dolan — obviously believe Vigneault’s record of 175-97-23 (.632) that includes a trip to the 2014 Cup final and the 2014-15 Presidents’ Trophy constitutes evidence worthy of reward.

Indeed, the Rangers have the fifth-most points in the NHL since Vigneault’s arrival and third-most in the East, 10 fewer than Washington and three fewer than Pittsburgh. The Blueshirts’ five playoff series victories under Vigneault are exceeded over the last three tournaments by only Chicago’s six and equaled by the Penguins and Lightning.

Vigneault’s Canucks won two Presidents’ Trophies and reached the Cup final in 2011 before losing a bitter seven-game final to Boston after holding leads of 2-0 and 3-2 in the series in which they held home ice. He has always favored an up-tempo style built on foundations of speed and skill; perhaps at times to the exclusion of some blue-collar toughness (Rat-a-tat, went Brad Marchand on Daniel Sedin’s face in Game 6 of the final) and thus to his teams’ detriment.

He depends on his team’s leadership group to set the off-ice standard, but he — by virtue of commands delivered in his high-pitched voice — is very much in command from behind the bench. Vigneault has been quicker this year to bench players, but that’s likely linked to the fact he has by far the most depth up front of his stay in New York, if not his NHL career that began in Montreal in 1997.

As well, Vigneault has succeeded in steadily integrating a group of young players into the mix. The Blueshirts have 10 players age 25 or younger slated to be in the lineup with an 11th, Kevin Hayes, sidelined by injury and a 12th, Adam Clendening, expected to be a healthy scratch.

In the midst of his fourth season in New York, the 55-year-old Vigneault is sixth in franchise coaching history with 295 games behind the bench, 24 fewer than Tortorella’s 319. His 175 victories are fourth-most, six behind Frank Boucher’s 181. Overall, Vigneault is 15th in NHL history with 597 victories.

But if Vigneault is under contract for the long-term, his focus will remain the same as he expects from his players. On one game at a time. And the schedule seems to be set up for the Rangers, who will play five of their first six out of the All-Star break at the Garden.

The question, though is whether it is more of a setup to fail, with a trap-door in the Broadway stage ready to open under this team that is 2-5 in the last seven on Broadway while going 6-1 on the road over the same span beginning Dec. 23.

For not only have the Rangers been losing regularly at the Garden, where they opened by winning eight of the first nine, they’ve often been less than competitive. Fact is, while being outscored 29-20 in those last seven at home, the Blueshirts have trailed by two goals four times after one period, and a fifth time by two goals within the first minute of the second period.

“Why? I can’t give a specific answer,” Vigneault said. “I don’t think we should be playing any differently, but it is what it is. Right now we have an opportunity to play a good game in front of our home fans. That’s all I can give you for now.”

Well, the coach does have through 2019-20 to come up with a better explanation than that.