Those would be the only two hits Baltimore would muster off Sale, who struck out eight in five innings.
Bundy looked strong out of the gate, needing only five pitches to get a 1-2-3 first inning.
He would cruise through the next three frames as well, but the Sox fought back in the fifth, tying the score on a two-out triple by Andrew Benintendi that scored Jackie Bradley Jr.
The wheels came off for the O's in the sixth as J.D. Martinez reached on a throwing error by Danny Valencia to lead off the inning.
Martinez would come around to score on a wild pitch, and Tzu-Wei Lin drove Mitch Moreland home with a double, giving Boston a 3-1 lead and forcing the Orioles' starter from the game.
It was the second consecutive start in which Bundy (0-2, 1.40 ERA) was saddled with a loss, despite allowing just one earned run and striking out six on Sunday.
"Anytime you have a guy throwing the ball like that, you want to give him some runs and take a little bit of pressure off of him," Baltimore first baseman Chris Davis said. "He's really risen to the occasion in every start that he's made this year. He's thrown the ball well, he's given us a chance to win and that's all you can ask of your starter."
After the first inning, only four Orioles batters reached base, one via a base hit, and only one of those reached scoring position, as they were unable to offer any opposition to the American League East leaders.
"You can talk about conditions, you can talk about the other pitcher, but we've got to swing the bats better," Orioles manager Buck Showalter said. "We know that."
COLD OPEN The gameday temperature was 34 degrees at first pitch. This season, the Orioles have dealt with first-pitch temps under 50 degrees in all but two of their games thus far.
"We've played very few games with the temperature above 55," Davis said. "It's kind of the way it goes. That's the old adage, 'The pitchers have the advantage the first month of the season.' It takes hitters a little bit to get their timing down. When you're battling the elements like this on a day-in, day-out basis, it makes it that much harder. But, we can't make any excuses. We've got to continue to work and we've got to continue to trust the process and understand that it's a long season and there's a lot of baseball to be played."
HE SAID IT "It's remarkable for me to watch him plying his trade in those type of conditions. I can't tell you how hard that is. That was impressive. I'm sure Dylan's done a little duck hunting in his life. That's kind of what that was like." -- Showalter, on Bundy working in the cold
UP NEXT With Monday's annual Patriots' Day at Fenway Park postponed, the Orioles now ship off to Detroit, where they will begin a three-game series against the Tigers starting on Tuesday at 6:40 p.m. ET. The added day could allow Showalter to adjust his pitching staff properly, as Thursday's probable is listed as TBD in place of Chris Tillman. Andrew Cashner is scheduled to be on the bump in Tuesday's series opener, with the Tigers countering with left-hander Francisco Liriano.
Craig Forde is a contributor to MLB.com based in Boston.