The Pittsburgh Steelers were down by 10 points, and down to their fourth and last running back. Somehow, they found an offense that was missing for most of three quarters and a way to win a game that easily could have been lost.

Jeff Reed kicked a 46-yard field goal in overtime and the Steelers withstood two season-ending injuries to key players and a bad first half to outlast the Ravens 23-20 on Monday night.

Reed’s third field goal — and his seventh career game-winner — ended a back-and-forth game in which the Steelers (3-1) were down 13-3 late in the third quarter, rallied but couldn’t hold a seven-point lead, then won despite being without their top three running backs.

‘‘We lost a lot of guys,’’ quarterback Ben Roethlisberger said. ‘‘I was more emotional, more vocal than I’ve ever been at halftime. I screamed at our offense. We were terrible in the first half. Not that we were great in the second half, but we bounced back.’’

The Steelers managed to win the game, but lost first-round draft pick Rashard Mendenhall (fractured left shoulder) and right guard Kendall Simmons (right Achilles) for the season.