The Ravens (3-2) had plenty of chances, but Joe Flacco threw a costly interception in the first half and the Browns blocked one of Justin Tucker's field goal tries.
Mayfield passed for 342 yards and threw a 19-yard TD pass in his first start at home. He completed a key third-down pass for 39 yards to Derrick Willies on Cleveland’s winning drive.
Joseph had badly missed a 55-yard field goal — toward the same end zone — with five seconds left in regulation, and the Ravens faked a kneel-down on the last play before the teams went to the 10-minute overtime session.
It was nothing new for the Browns, who tied Pittsburgh 21-21 in the opener and lost 45-42 last week in Oakland in a game they led by 14 points in the second half.
And after so many mistakes by its special teams, Cleveland finally got a decisive play to win.
The Ravens, who got another strong effort from their defense, also had a chance to win it in the final minute of regulation, but wide receiver Michael Crabtree couldn’t hold onto Flacco’s pass in the back of the end zone.
Tucker then tied it with a 32-yard field goal with 52 seconds left.
On their third possession of OT, the Browns started at their own 5-yard line and were at their 18 facing a third down when Mayfield zipped a pass over the middle to Willies, who didn't have any catches coming in and was playing after Rashard Higgins went out with a knee injury.
Duke Johnson ripped off a 15-yard run and had two more short carries before the Browns sent in Joseph, who was released by Miami after training camp but got a another chance after Gonzalez missed four kicks in a Week 2 loss at New Orleans.
Cleveland's win was also the Browns' first in 37 tries on a Sunday, and it gave Jackson his first victory inside the division in three seasons.
Beyond that, the Browns again showed they've made major progress following a winless season. It was their first win against a division opponent since Oct. 11, 2015, at Baltimore.
Flacco finished 29 of 56 for 298 yards and one interception, but Baltimore’s offense struggled to get into a rhythm all day.
Cleveland's league-leading 15th takeaway put the Browns in position to become the first team to score a second-half TD on the Ravens this season.
However, Baltimore's defense stiffened with its backs at the goal line and the Ravens sacked Mayfield on third down. The Browns settled for Joseph's 35-yard field goal to take a 9-3 lead midway through the third quarter.
Mayfield's 19-yard TD pass late in the second quarter gave the Browns a 6-3 lead.
Backed up with bad field position for most of the first half, Mayfield drove the Browns 78 yards for the go-ahead score with 40 seconds left. Mayfield completed consecutive passes down the seam to tight end David Njoku before showing poise under pressure and delivering his strike to a wide-open Higgins.
Joseph missed the extra point, but the Browns got another big play by Denzel Ward, their other first-round pick, who blocked Tucker's 48-yard attempt to end the half.
Cleveland's defense was solid last season, but didn't force enough mistakes. That's changed as the Browns now lead the league with 15 takeaways after recording 13 all last season.
Cleveland was called for 10 penalties, while Baltimore was only whistled for three, but one of them came in overtime and wiped out a big run by Alex Collins.