OTTAWA — After a gut-wrenching overtime loss here for the second consecutive Saturday, the Rangers’ backs are against the wall.

Kyle Turris scored at 6:28 of overtime with a shot through Henrik Lundqvist’s pads as the Senators beat the Rangers, 5-4, in Game 5 to take a 3-2 lead in the best-of-seven series.

Game 6 is Tuesday night at Madison Square Garden.

The Rangers are on the brink of elimination because they couldn’t protect another late lead in Ottawa. They led 4-3 before former Ranger Derick Brassard tied it with 1:26 left in the third period after the Senators pulled goalie Craig Anderson for an extra attacker.

“We can’t lose another game,” coach Alain Vigneault said.

In a game of missed opportunities and numerous goals scored from in front, the Blueshirts came very close to winning early in overtime. J.T. Miller’s shot went off Anderson and hit the crossbar with less than four minutes gone. Then Michael Grabner deflected a shot past Anderson at 4:12, but the goal was waved off because his stick was above the height of the crossbar when he made contact with the puck.

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Rookie Jimmy Vesey scored his first career playoff goal with 7:12 left in the third period to give the Rangers a 4-3 lead, but their defensive structure again cracked in the waning minutes. Brassard, who skated as the extra attacker when Anderson was pulled, tied it when his pinballing shot bounced off Tanner Glass and Brendan Smith’s skate before trickling past Lundqvist (32 saves). It was Brassard’s first goal of this series.

“We’ve played our best hockey coming home and being desperate,” Marc Staal said. “Now we’re one game away from being out of it. We know it’s going to be there, we’re going to be there. We’re going to respond the right way and get this thing back in Ottawa.”

The Senators, who have considered themselves underdogs since Game 1, are one win away from reaching the Eastern Conference finals for the first time in 10 years. The Senators are 4-0 all-time in overtime against the Rangers and 5-1 in overtime in this year’s playoffs.

“We know it’s going to be very difficult,” Senators coach Guy Boucher said. “They have a lot of tools; we have to figure out how to be better than the last two times we’ve been there.”

It was the second straight overtime loss at Canadian Tire Centre for the Rangers, who led the NHL in road wins during the regular season. The Senators also rallied to win Game 2 in Ottawa, 6-5, in double overtime after the Rangers coughed up three two-goal leads, including 5-3 in the last few minutes of regulation.

The Rangers took a quick 2-0 lead. Jesper Fast finished an odd-man rush just 4:07 into the game and defenseman Nick Holden beat Anderson (29 saves) at 5:13, temporarily silencing the crowd.

But in what turned out to be a jump-start for a pushback by the Senators, Mark Stone scored off a scramble in front after Lundqvist’s fumble behind the net, cutting the Rangers’ lead to 2-1 at 6:03 with the third overall goal in 1:56 and grabbing the momentum.

The Senators scored two goals in 33 seconds in the second period to take a 3-2 lead. Mike Hoffman one-timed a pass from the right circle at 8:17 and Tom Pyatt’s tip slid under Lundqvist.

The Rangers tied it at 3 after a strong shift as a turnaround shot by Michael Grabner off a loose puck was nudged in by Ryan McDonagh at the right post to tie it at 3 with 2:11 left in the second period.

Vesey, who assisted on Holden’s goal earlier, got just enough of the puck past the goal line before Anderson reached back to grab the puck with his glove. The goal initially was waved off on the ice, but a review quickly reversed the call, as replays showed the puck clearly was over the line.

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But the Rangers again could not hold the fort. Brassard, who was traded for Mika Zibanejad last summer, joined the play in the offensive zone and kept the Senators’ hopes alive.

“We’re in this situation together here,” McDonagh said. “I guarantee you we’re not going to quit. We just have to refocus here, get rejuvenated. We’ve got to win a hockey game at home. That’s all we’ve got to focus on.”