The Ravens, who led 13-3 late in the third quarter, lost for the seventh straight time in prime time.
The key play in overtime came on third-and-eight, when fourth-string running back Mewelde Moore delivered a 24-yard catch to set up Reed's game-winner.
"We had it," receiver Derrick Mason said. "In this game, you got a full 60 minutes of football. I'm not big into moral victories."
The Ravens fell to 2-1 and gave the AFC North lead back to the Steelers (3-1) in a game that turned late in the third quarter.
In a 15-second period, the Ravens collapsed on offense and defense, allowing a 13-3 lead to turn into a 17-13 deficit.
First, the NFL's top-ranked pass defense flinched after crushing quarterback Ben Roethlisberger throughout the game. Beating cornerback Fabian Washington over the middle, Santonio Holmes bounced off a Chris McAlister tackle and then sidestepped Ed Reed for the 38-yard touchdown.
On the next offensive play from scrimmage, Joe Flacco looked like a quarterback starting his first road game. He made a costly fumble after being hit from behind by linebacker James Harrison. Steelers linebacker LaMarr Woodley rolled on the ground to get the loose ball before getting up and running 7yards for the score.
"I was just trying to throw the ball away," said Flacco, who finished 16-for-31 for 192 yards and one touchdown. "If I take care of the ball, it's a different story."
The Ravens, who allowed 20 points in their first two games, surrendered 14 points in two plays from scrimmage.
But after Pittsburgh went ahead 20-13, the Ravens responded in the fourth quarter behind Flacco and Mason. The two connected on passes of 15, 10 and 35 yards (which converted third-and-12) before Le'Ron McClain bowled over Lawrence Timmons for a 2-yard touchdown.
That tied the score at 20 with 4:02 left in the fourth quarter.
The Ravens won the coin toss but punted after Flacco was sacked. The Steelers then drove 29 yards on seven plays for their 14th straight home win on Monday Night Football.
"There is nothing you can say about this game other than the fact that a couple of plays went against us," Ravens coach John Harbaugh said. "Beside that, our guys played well enough to win."
In the first half, it was hard to determine which team was starting the rookie quarterback.
Roethlisberger, a Super Bowl-winning quarterback, continually made more mistakes than Ravens first-round pick Flacco.
Roethlisberger threw an interception to 6-foot-4, 345-pound defensive lineman Haloti Ngata. He crumbled against the Ravens' pressure, tripping over his feet one time and even losing his shoe.
The Ravens took advantage of Roethlisberger's struggles to dominate a Steelers offense that was without injured starting running back Willie Parker.
Outside of Pittsburgh's first drive (a 45-yard one that ended with a 49-yard field goal), the Ravens held the Steelers to 1 net yard and no first downs for the rest of the first half. That spanned five drives and 21:44.
After Ngata's interception at midfield - the ball seemed to slip out of Roethlisberger's hands - Flacco completed passes of 18, 6 and 14 yards. The drive stalled on two incompletions, but his pass to Mason was close to a touchdown.
It appeared Mason got both toes in the end zone while falling out of bounds, but the Ravens didn't challenge. A 33-yard field goal by Matt Stover tied the game at 3 late in the first quarter.
The Ravens reached the red zone for the first time in the second quarter, but they made an interesting play call on third-and-goal. Instead of passing, the Ravens chose to run a draw with Willis McGahee, who had been injured five plays earlier.
He was stopped at the 2-yard line, forcing Stover to kick a 20-yard field goal to put the Ravens ahead 6-3.
On the next drive, the Ravens didn't settle for another field goal. Le'Ron McClain took a short pass and delivered a 25-yard catch, cutting back to avoid two Steelers defenders to get the Ravens to the Pittsburgh 3.
On second-and-goal, the Ravens had to run up to the line because the play clock was close to expiring. After getting the play off with only a few seconds to spare, Flacco dropped back and dropped in a 4-yard touchdown pass to tight end Daniel Wilcox in the left corner of the end zone.
Flacco's first career touchdown pass extended the Ravens' lead to 13-3 with 17 seconds remaining in the second quarter.