The Red Sox don’t find themselves in many pitchers’ duels these days, boasting the highest-scoring offense in the Majors. But on Tuesday, for the second time in as many nights, runs were at quite the premium with Nathan Eovaldi and Chris Bassitt on the mound.

Eovaldi kept Boston in the fight, tossing six innings of one-run ball in a 3-2 loss to Oakland on Tuesday night at Fenway Park. He also extended his MLB-best homerless streak to 58 innings, dating back to last year, and claimed the third-longest homerless streak to begin a season (45 innings) in the past quarter-century of Red Sox history.

For the second straight night, though, Boston’s offense and bullpen couldn’t match its starter’s efforts.

On Monday in Baltimore, the Red Sox turned to their bullpen in a 1-1 game, and reliever Matt Andriese immediately allowed the eventual winning run. This time, Darwinzon Hernandez entered a 1-1 game in relief of Eovaldi -- who threw a season-high 102 pitches -- and coughed up a pair of runs to the first three batters.

The left-handed Hernandez, pitching for the first time since blowing a save last Thursday, entered to face Oakland’s 4-5-6 hitters. Red Sox manager Alex Cora called it a “good pocket” for Hernandez, though, because two of the first four batters he was set to face were left-handed (plus a switch hitter).

“He was wild today,” Cora said of Hernandez. “He put himself in a tough spot.”

Indeed, Hernandez lacked control with his fastball, and it got him in trouble. He walked Matt Olson on five pitches and allowed a 1-2 single to Jed Lowrie in the next at-bat.

If not for the three-batter minimum rule, that might’ve been the end of his night. Instead, Hernandez had to stay in to face righty Matt Chapman, who singled in Olson to give the A’s the lead.

In some small-sample weirdness, Hernandez has struggled at home this season -- eight runs, six earned, in five innings -- while tossing 6 2/3 scoreless innings on the road. Cora didn’t know what to make of that when he found out.

“We’ve gotta use him in spots, regardless if it’s on the road or at home,” he said. “[I’ll] probably talk to the player and see what’s going on.”

For what it’s worth, Hernandez had no theories on the matter.

“It’s never something that’s on my mind,” he said.

With two games left in this series, the Red Sox and A’s now share the lead in the American League standings. On most nights, Boston’s high-octane offense does enough to help the team win. Sometimes, the rotation carries the load. The bullpen, on the other hand, is lagging behind. 

In the past 10 games, Boston’s relievers have pitched to a 6.35 ERA (24 earned runs in 24 innings), with six home runs allowed. In the past week, they’ve taken three losses and blown a save. 

Closer Matt Barnes is eight-for-eight in save situations and has allowed just one hit versus 12 strikeouts over his past seven outings. But the path to get to him, once the starter is finished, has never been murkier.

“We’re searching,” Cora said in regard to figuring out the late innings. “You’ve seen it. Obviously, we do feel very comfortable with some of the guys back there … But we need [others] to be more consistent. When that happens, the structure is gonna be a lot easier.” 

Despite a lapse from the bullpen, Boston nearly pulled off a win with some ninth-inning drama. The Red Sox walked twice against A’s reliever Jake Diekman, but they stranded runners on the corners with a game-ending popout from Christian Vázquez. 

So here’s the silver lining: Despite a hapless night at the plate, Boston was in it, right to the end. The bullpen struggles, though, must be extinguished soon. 

“As you guys know, bullpens go up and down,” Cora said. “Sometimes they’re great for three weeks, and then they struggle for three days, you know? And then we get it back.”