That was an accomplishment, because the Orioles had entered Monday with 148 runs in the seventh inning or later, the most in the American League. The bullpen, which had two All-Stars in Zach Britton and Brad Brach, tends to make comebacks possible.

Britton has converted all 29 of his save chances. Only one left-hander has ever started a season with a longer streak, and he was named his league’s most valuable player: Willie Hernandez of the 1984 Tigers. Britton cited the Orioles’ late-strike ability, and the bullpen’s success in making those late runs matter, as reasons for the team’s record.

He also mentioned pitcher Chris Tillman, who has been the only reliable starter on the staff. The Orioles’ rotation has a 5.10 earned run average; through Sunday, its E.R.A. ranked ahead of only Minnesota and Cincinnati, two of the majors’ worst teams. (The Orioles’ bullpen E.R.A. is 3.03.)

“Tillman’s really stabilized our rotation, and it’s been a tough thing to ask from him, to really have to be on top of his game every time out,” Britton said. “You think about the pressure he’s got, every time he takes the ball, and he’s done a great job.”

Tillman, who starts the series finale on Thursday, is 13-2 with a 3.29 E.R.A. The quality start may be a low standard to meet — at least six innings, no more than three earned runs — yet in the 71 games Tillman has not started, the Orioles have managed just 24 quality starts.

They have made changes. Dylan Bundy, the fourth overall pick in the 2011 draft, made his first career start on Sunday. Vance Worley, a veteran who has been working in long relief, starts Tuesday in place of Ubaldo Jimenez. The Orioles lavished a four-year, $50 million contract on Jimenez — or $1 million for each of his A.L.-leading 50 walks this season — that runs through 2017. Now, with a 7.38 E.R.A., he has no clear value to the team. Perhaps Worley can be an answer, but the Orioles badly need to upgrade their rotation before the Aug. 1 nonwaiver deadline.

The Red Sox did so last week by trading for the All-Star Drew Pomeranz from San Diego, following deals for closer Brad Ziegler from Arizona and infielder Aaron Hill from Milwaukee. The Orioles have been quiet so far, but their players understand the calendar.