He entered in the ninth inning with a 7-5 lead and allowed two runs on three hits before being pulled. The Orioles were able to recover and pull off an 8-7 win in 12 innings.
Britton gave up three straight hits before a sacrifice fly by A's outfielder Matt Joyce tied it. Following a walk to Khris Davis, Britton was replaced by Miguel Castro (3-1), who quelled the uprising and kept Oakland at bay to the finish.
"I was pretty disappointed,'' Britton said. "Just wasn't very good at all today. Where we are right now, you want to win those games, and obviously we did, and it's because of Castro.''
Manny Machado led off the 12th with a home run off Simon Castro (1-2) to end a game that lasted 4 hours, 20 minutes.
Britton's last blown save was Sept. 20, 2015, at Tropicana Field against the Rays. Britton finished well short of Eric Gagne's major league mark of 84, set from 2002 to '04.
"I just called him in my office and congratulated him. You won't see it again,'' Orioles manager Buck Showalter said.
In an apparent reference to Gagne's admitted usage of PEDs during his career, Showalter added "And [Britton] does hold the record in my mind, OK?''
"I didn't make quality pitches today and that's the gist of it really,'' Britton said. "If you get beat with good pitches, I think it's a different feeling. But, you know, today just wasn't sharp at all from the get-go.''
Britton confirmed after the game that he will get an MRI on his left knee, which has been giving him trouble since 2014, but would not blame his ineffectiveness on the injury.
"I pitched through it the last three or four years,'' he said.
The Associated Press contributed to this report.