RALEIGH, N.C. — Before they left for San Jose 12 days ago, the Flyers’ Sean Couturier called it a road trip that could determine “where our season can go one way or the other.”

Eleven days later, that direction appeared to be closer toward a golf course than a playoff run in early April, but a point salvaged in an overtime loss to the Carolina Hurricanes took some of the heat off what had otherwise been a miserable two weeks.

The Flyers on Tuesday squandered a two-goal lead, fought back from a two-goal deficit and eventually lost in overtime when All-Star defenseman Dougie Hamilton beat Brian Elliott and the Flyers, 5-4.

The road trip ended 1-4-1.

Travis Sanheim tied it with four minutes left to assure the Flyers would get at least one point. It was just the second time the Flyers managed a point when trailing after two periods on the road. They had been 0-13-1 going in.

“We know we have to play better, especially on the road,” said Jake Voracek, who was the Flyers’ best player Tuesday night. “But now we’re going home. All those tough road trips, the [arduous] traveling is behind us now. Now we’ve got to focus on taking it up a notch for the second half of the season.”

The Flyers are 22-15-6 and have 39 games left as they try to get back into the postseason. They are a point ahead of Florida, which lost Tuesday night, for the final spot in the East.

While the Flyers will play six of the next seven at home, things don’t get any easier. They turn right around on Wednesday and host Washington in a national TV game (7:30 p.m., NBCSN). The Capitals lead the league with 65 points after dusting Ottawa 6-1 on Tuesday.

“We played better, played harder,” said Matt Niskanen. “We still made mistakes, but I thought we showed some guts coming back to get a point out of that. Would have loved the win, but it’s a step in the right direction.”

The Flyers have been plagued by goals against in quick spurts. Happened again Tuesday as the Hurricanes hit twice in 1 minute, 45 seconds during the second period.

Nic Aube-Kubel scored the Flyers’ only goal in the second, a tally that came off a turnover. Shayne Gostisbehere hit the crossbar on a blast that would have tied it. It was obvious the Flyers’ plan was to shoot high on Carolina’s James Reimer, who did not look comfortable for much of the evening.

Elliott allowed five goals on 33 shots. Hamilton’s overtime goal came after Travis Sanheim lost his stick. If you think three-on-three is a fire drill, try three-on-two-and-a-half.

Elliott saw 16 shots in the first period, stopping 14. He denied dangerous wizard Andrei Svechnikov on a breakaway and Warren Foegele on a split save that left him dazed when Foegele hit him in the head. Elliott briefly stayed down, but got back up and remained in the game. Elliott received treatment following the game and was not immediately available.

The Flyers came into the game having been outscored 13-3 in the first period in the first five games of this trip (four losses). They opened a 2-0 lead on a soft goal by Travis Konecny (who might have been the second-best Flyer) and a nice one by Michael Raffl off a feed from Voracek. Raffl set up the play by forcing the 'Canes into a turnover with a good forecheck.

It was Raffl’s first goal in 24 games, dating to Oct. 26. Voracek picked up his seventh assist in five games.

The players quickly hustled out of the arena as equipment man Harry Bricker and his staff packed things up for one final flight. This one was headed to Philly International. Finally.

“We took a step in the right direction,” coach Alain Vigneault said. “Now we gotta get home -- not that I don’t like talking to you guys [in the media], but we gotta get home and play tomorrow.”

And with that, he hustled off. Vigneault wasn’t happy with the result, but he did look relieved.