The Wizards rallied from a six-point halftime deficit with a big third quarter and then came through down the stretch to successfully open a four-game road trip.
Miles Plumlee hit a hook shot with 2:43 to play that lifted the Suns into a 93-93 tie and Beal took over from there.
His 3-pointer came with 2:03 to go and put Washington in front for good. He added a jump shot with 27 seconds remaining to give the Wizards a four-point lead and finished things off with a rebound and dunk that accounted for the final score.
Goran Dragic led Phoenix with 19 points and 11 assists. The Suns had won their previous two games.