Cleveland (2-3) had lost 13 of the previous 14 meetings in this AFC North rivalry and was winless in Baltimore since 2007. The final score of that game, by the way, was 33-30 in overtime.
In this one, McCown rallied the Browns from a 12-point deficit to leave the Ravens (1-4) alone in the division cellar.
"A little closer than you'd like," McCown said, "but the outcome certainly was fitting and we'll take it."
Playing its second straight overtime game, Baltimore went three-and-out on the first possession of the extra period. McCown then used more than seven minutes to move 51 yards before Coons kicked his fourth field goal of the game with 6:43 left.
McCown completed 36 of 51 passes with two touchdowns in becoming the first quarterback in Browns history with three straight 300-yard games. He broke the team record of 444 yards passing set by Brian Sipe on Oct. 25, 1981, against the Baltimore Colts.
McCown knew for days that the Browns could take advantage of a porous Baltimore defensive backfield.
"Wednesday," he said. "We love throwing the ball around. So we're ready to roll."
The Ravens, on the other hand, are spiraling. Baltimore never before has been 1-4, and this marks the first time the Ravens lost their first two games at home — both against division foes.
"It's not going to be a matter of, 'How do we handle this adversity of being 1-4?' We'll handle it," coach John Harbaugh said.
Joe Flacco ran for two 1-yard touchdowns and threw for a score, but fell to 13-2 against Cleveland. After going to the postseason in six of the past seven years, Flacco and the Ravens are in a unique bind.
"It doesn't feel too good," Flacco said.
Baltimore went up 27-22 on a 1-yard run by Justin Forsett with 5:56 left, but the Ravens couldn't come up with the big play in the fourth quarter.
McCown connected with Isaiah Crowell on a 22-yard touchdown pass with 3:03 remaining, and the 2-point conversion left the Ravens needing a field goal to tie.
A personal foul against Donte Whitner on a third-and-6 incompletion led to a 32-yard pass from Flacco to Forsett, who hurt his right ankle on the play. He finished with 121 yards rushing.
"I felt like if I went back out there I possibly could have damaged it more," Forsett said.
After Forsett left, three plays inside the 10 failed to get the ball into the end zone. That left Justin Tucker to kick a 23-yard field goal with 25 seconds to go in regulation.
Overtime belonged to the Browns after a wild fourth quarter.
"You have wins that define things for you — that can define a season or be a turning point — and we hope that was this for us," coach Mike Pettine said.
Down 21-9, the Browns rallied behind McCown to take a 22-21 lead with 12:23 remaining.
First, he directed a 13-play, 75-yard drive that was extended by a hands-to-the-face penalty call against Jason Babin on a third-down incompletion from the Baltimore 15. Two plays later, McCown ran in from the 10.
After a Baltimore punt, McCown needed only four plays to cover 79 yards and give Cleveland its first lead. Following a 56-yard completion to Andrew Hawkins, McCown lofted a pass toward the end zone that tight end Gary Barnidge and safety Will Hill each had an equal chance to catch.
The ball glanced off Burnidge's left leg and rolled down to his left ankle as he pinned his legs together to control it. While on his back, he reached down and secured the ball for an 18-yard touchdown.
It turned out to be merely the opening salvo of a wild fourth quarter.
Notes: Ravens WR Steve Smith (back) and tight end Crockett Gillmore (calf) were inactives. They were ultimately joined on the sideline by linebacker Elvis Dumervil (groin) and defensive backs Lardarius Webb (thigh) and Will Davis (knee). ... Cleveland CB Joe Haden played with a broken right ring finger. He banged his head early in the fourth quarter and was kept out with a concussion.