Coleman had a career night as he rushed for 181 yards and a score in helping to lead the Husky offense to 352 yards rushing on the night and 512 yards of total offense.
QB Jake Browning finished the night 14 of 21 for 160 yards with two touchdowns and an interception, but it was his final pass, a four-yard touchdown to WR Dante Pettis in the first overtime, that sealed the deal for the Dawgs.
Washington's defense struggled all night trying to stop Arizona QB Brandon Dawkins who finished with 176 yards and two scores on the ground while completing 19 of his 31 attempts for 167 yards with a touchdown and an interception.
The Huskies missed on two field goal attempts by K Cameron Van Winkle and they also struggled with eight penalties for 63 yards.
Arizona got off to a fast start, scoring the first two times they had the ball with Dawkins and RB J.J. Taylor, who rushed for 97 yards and a touchdown before going down with an ankle injury, each scoring.
Washington's defense was on the heels for most of the first half, but they did manage to stop the Wildcats on fourth and goal from the one and that seemed to stem the tide of the early Arizona onslaught for at least a bit.
WR John Ross III was his typically dynamic self as he had one carry for 32 yards and a touchdown, a nifty tight-rope run along the sideline on a reverse, and he also had four receptions for 28 yards and another score.
The Huskies held Arizona to just 22 yard in the third quarter and appeared poised to pull away, but missed opportunities allowed the Wildcats to stay in the game.
Coleman busted off a 55-yard touchdown run that gave the Huskies the lead 28-21 with a little over three minutes left on the clock.
On 2nd and 25 from the Arizona 32, Husky defensive lineman Vita Vea had the chance to bring Dawkins down for a big loss, but sophomore stayed on his feet and hit WR Shun Brown for a 54 yard gain which put the Wildcats in position to score the game-tying touchdown with just :12 left on the clock.
In overtime, the Huskies got the ball first and after Coleman ripped off another impressive run that gave the Dawgs a first and goal at the two yard line, Browning hit Dante Pettis with the game-winner three plays later.
On Arizona's ensuing possession, the Wildcats faced fourth and 10 from the Washington 11.
Dawkins was unable to handle the bad snap, but eventually picked it up and rolled right.
He threw the ball up for grabs, but it was knocked away, giving the Huskies the win.
Washington, now 4-0, will face Stanford on Friday night at Husky Stadium in a battle of unbeatens and the inside track in the Pac 12 North race.