"That was awesome," Brady said, "pretty sweet."
The improbable rally salvaged a potentially costly day for the Patriots (10-3), who lost star tight end Rob Gronkowski to a suspected torn anterior cruciate ligament in his right knee in the third quarter. He is expected to undergo an MRI on Monday.
New England fell behind 19-3 when Jason Campbell connected with Josh Gordon for an 80-yard touchdown late in the third. Campbell's third scoring pass of the day, a 4-yarder to Jordan Cameron with 2:39 left in the game, made it 26-14.
That's when Brady engineered the impressive comeback that kept the Patriots in front in the race for the No. 2 playoff seed in the AFC. Had New England lost, Cincinnati would have moved into the second position.
"How many times has he done that in his career?" Browns coach Rob Chudzinski said after his team's seventh loss in eight games. "We had our opportunity and we weren't able to close the game out how we wanted to."
Brady threw a 2-yard scoring pass to Julian Edelman with 1:01 left and a 1-yarder to Danny Amendola with 31 seconds remaining.
The Browns (4-9) had one last chance, but Billy Cundiff missed a 58-yard field goal attempt on the final play.
"We had to make just about every play that we made at the end today," Patriots coach Bill Belichick said, "and, fortunately, we did."
They cut the deficit to 26-21 on Edelman's touchdown. A 15-yard penalty against the Browns for unnecessary roughness on Edelman allowed the Patriots to kick off from the 50-yard line, rather than their 35.