– The Twins thought they had Sunday’s game won in the eighth inning, when Brian Dozier blasted a three-run homer off Stephen Strasburg.

Then Twins thought they had the game won in the 15th, when Miguel Sano smacked a two-out RBI single for another lead.

Both times they were cruelly denied.

The Nationals wouldn’t let the Twins escape with a victory. Tying the score in the ninth inning on a Bryce Harper pinch-hit home run, tying it again in the 15th on catcher John Ryan Murphy’s throwing error, Washington finally won 6-5 on Chris Heisey’s home run off Michael Tonkin in the 16th inning.

Punched in the gut and kicked in the teeth, the Twins retreated to the Twin Cities after being swept in the three-game series. They completed a 1-4 interleague road trip that, combined with their six losses at Baltimore and Kansas City to open the season, put their road record at 1-10.

Twins manager Paul Molitor has to sift through the smoldering remains of a bullpen that scarred and charred after giving up big blows late. And at 5-14, his club has the worst record in the American League and is tied for the most losses in baseball.

“We talk about adversity all the time,” Molitor said, “and that’s where you get tested the most, and we’re being challenged here early on as to what kind of resiliency we are going to show.”

It was the 20th time in club history the Twins have played at least 16 innings, the first time since they went 16 on July 3, 2009, in an 11-9 home loss to Detroit. Of those games, Sunday’s contest of 5 hours, 56 minutes was the third-longest, timewise.

And the Twins struck out 20 times to set a club record for most strikeouts in an extra-inning game. It came one day after the Twins tied their nine-inning strikeout record of 18.

The Twins went hitless from the ninth inning until the 15th, when Eduardo Nunez singled with two out for his fourth hit, then stole second — he was originally called out, but the Twins challenged and won. After a walk to Dozier, Sano, 0-for-6 with four strikeouts at that point, delivered an RBI single on reliever Yusmeiro Petit’s 77th pitch.

Ryan O’Rourke, in his fourth inning of relief, started the bottom of the inning and got two outs before walking Danny Espinosa. With lefthanded-hitting Oliver Perez — a pitcher, whose last plate appearance came in 2010 — due up, Molitor decided to go with Michael Tonkin, his last reliever available, for a one-out save.

“I wasn’t excited about putting O’Rourke back out there for the fourth inning,” Molitor said. “I think he went out there with guts, pretty much. I had a chance to get one out there with the pitcher [due up]. I thought it was my time to pull my last bullet out.”

Espinosa stole second on Tonkin’s first pitch. On a 1-1 pitch, Perez dropped down a bunt.

Murphy sprung from behind the plate to grab the ball as it rolled up the third-base line, but he threw wildly to first, past Joe Mauer. Espinosa scored the tying run. The ball might have rolled foul had Murphy let it go.

“That’s what I was trying to figure out,” Murphy said. “If the ball was going to go foul or stay fair.”

Tonkin, who pitched three innings Friday, went back out for the 16th and Heisey soon ended the game. Tonkin threw a hanging breaking ball that Heisey didn’t miss.

“Obviously it is tough,” Tonkin said. “It’s frustrating. A lot of guys are out there grinding away, busting their tail. To not be able to finish it off is frustrating.”

It was the second time in the game the Twins weren’t able to finish it off. In the eighth inning, Dozier followed singles from Mauer and Nunez by launching a 95-mile-per-hour fastball from Strasburg into the seats for a 4-1 Twins lead. But Trevor May gave up two runs in the bottom of the inning to make it 4-3. In the ninth, Harper — who was supposed to get the day off — pinch hit to lead off against Kevin Jepsen and obliterated a fastball over the center-field wall for his ninth homer of the year.

The Twins were supposed to announce roster moves after game, as Danny Santana will be activated from the disabled list Monday. But Molitor has to figure out the state of his bullpen.

“There will be some spinning,” Molitor said. “On the plane ride.”