BOSTON — The Mariners not only scored a run, but they won a game. Neither was a certainty given their recent showings on this road trip. But after being shut out on back-to-back days at hitter-friendly Fenway Park, something no Mariners team had happen before, Seattle managed to direct more than a few baserunners to home plate, making sure a brilliant pitching performance from starter Christian Bergman wasn’t wasted in a 5-0 win over the Red Sox on Sunday.

The Mariners avoided being shut out and swept in Boston, improving to 22-29 on the season. They head to Denver for a brief two-game set at Coors Field against the National League West-leading Rockies.

“It hasn’t been easy for us,” manager Scott Servais. “It’s been a struggle. I think yesterday we hit rock bottom. And the only way you get off the bottom is to start crawling up.”

Can one win get the Mariners going again?

“I hope, man,” said Robinson Cano. “Hopefully this is the game that wakes us up and we can win some games because we need that so bad.”

Less than 24 hours earlier, Nelson Cruz called their showings in Boston and overall performance “embarrassing.” And it was a deserved label considering the results. There was a noticeable anger in the players on Saturday night after being shut out by lefty Brian Johnson, who was making a spot start and optioned to Class AAA Pawtucket after his gem.

“Sometimes you have to get mad at yourself,” Cano said. “You don’t want to be in this position when you know you have the talent to compete with anyone. To get shut out twice? It’s not like we were facing Chris Sale. We should have been playing better.”

Seattle came back with a performance not to be ashamed of, starting with Bergman, who pitched seven shutout innings, allowing four hits with two walks and two strikeouts. Meanwhile, the recently-maligned and anemic offense banged out 16 hits in the game. The only negative was stranding nine runners and not scoring more.

“It was really a struggle to get five runs today considering all the traffic we had out there,” Servais said. “But we got a lot of hits and I thought our offensive approach — we were much aggressive on the fastball and guys showed up ready to play today. It was good.”

Bergman was better than good. Considering the team he was pitching against and in the confines of Fenway, it might have been his best big league outing.

“I can’t say enough about the effort he gave us today,” Servais said. “He was throwing strikes and attacking the strikezone and that’s what you have to do in this ballpark and against this team.”

In his previous start, the veteran right-hander struggled with wandering command and far too much solid contact, giving up 10 runs in four innings pitched, including eight in one inning. But this was more like the version of Bergman that threw the 7 1/3 scoreless innings against the A’s two starts earlier. He wasn’t dominant, but efficient in pitching to contact — mostly ground balls. He had runners on base in each of his first five innings pitched, but double plays in each of the first four innings allowed him to escape without allowing a run.

“I couldn’t wait to get back out there after last time,” Bergman said. “Sometimes the best way to move on is to get back out there, simplify everything and get back to making pitches.”

Besides ending innings and keeping his pitch count in check, the double plays helped Bergman find a rhythm. He worked at a quick pace, something his teammates loved.

“Bergy threw the ball great,” said third baseman Kyle Seager. “He works fast. He goes right at people. He’s on the mound and ready to throw it. He gets ahead early and throws strikes. He’s a lot of fun to play behind.”

After 23 consecutive innings without a run, the Mariners broke their scoring drought in a fitting way — without a run-scoring hit. Seager doubled with one out in the fourth off of Red Sox starter Rick Porcello, moved to third on Danny Valencia’s single and scored on a wild pitch to make it 1-0. The one run didn’t initially open the floodgates for more. Seattle loaded the bases with two outs, but Porcello struck out Jean Segura to end the inning.

Not looking to wait another 23 innings for a second run, the Mariners added another in seventh. Carlos Ruiz, who had just six hits on the season, doubled off the Green Monster for his third hit of the game to start the inning. He later came around to score on Nelson Cruz’s two-out single up the middle that was gloved by a diving Xander Bogaerts, but thrown away at first.

“I’m just happy that we got a W and as a team we were fighting together,” Ruiz said. “I was just trying to have some good at-bats and forget what has been happening the last two or three days.”

Given the hitting woes of the past 15 games — 2.25 runs per game, .205 team batting average and .575 team on-base plus slugging percentage — Seattle turned it into an offensive explosion in the eighth. Guillermo Heredia jumped on a 1-0 slider from reliever Heath Hembree, hammering his third homer over the Green Monster and out of Fenway to make it 3-0.

“It was just good contact,” Heredia said through interpreter Manny Acta.

The game turned into a Mariners’ version of a rout in the ninth inning when Robinson Cano, undaunted by the slow pace of pitcher Fernando Abad and the five trips to the mound from catcher Sandy Leon, hammered a two-run homer to center. Cano’s ninth homer of the season made it 5-0. After going 1-for-11 against Abad in his career, Cano has now homered in two straight at-bats against the lefty specialist, belting one last season.