Beal finished with 25 points and John Wall had 17 points and 13 assists for Washington. Wall had 13 points in the fourth quarter, and the duo scored the Wizards' last 15 points.
Otto Porter added 19 points to help Washington win its second straight over San Antonio dating back to last season. The Spurs had previously won 17 straight against the Wizards.
Kawhi Leonard led San Antonio with 23 points and Tony Parker scored 11 of his 17 points in the fourth quarter. LaMarcus Aldridge had 10 points and 14 rebounds for the Spurs, who committed 21 turnovers and had their three-game win streak snapped.
After losing their lead late in the fourth quarter, the Spurs tied it three times, the last coming when Parker sank a 3-pointer from the right wing to make it 99-all with 7.9 seconds left.
The Wizards called two timeouts in setting up their inbounds play. Eventually they got the ball to Wall, who dribbled and found Beal in the right corner, where he sank his shot over a leaping defender.
The Wizards, who had an early 17-point lead, used an 11-3 run to take their first lead since the first quarter to set up the final sequence.
They closed within one when Marcin Gortat took Wall's full-court feed and dunked over the leaping Danny Green. Two possessions later, Wall's 3-pointer from the left corner tied it at 90-all before Beal's dunk following a transition feed from Porter made it 92-90.
Spurs: F Tim Duncan played in his 1,336th NBA game, moving ahead of Gary Payton for 10th all-time. . Parker made his 1,000th NBA start. . The Spurs made their first 11 free throws before Boris Diaw missed the first of two with 33 seconds remaining in the third quarter.
Wizards: The Wizards have allowed at least 50 points in every first half this season after allowing 51 to the Spurs. . Wall's 13 assists were his most since registering 14 at Memphis on April 4 last season.
New Washington Nationals manager Dusty Baker received a hearty ovation when he was shown on the videoboard sitting in a lower-level suite with general manager Mike Rizzo. Baker will be officially unveiled at a press conference Thursday.
Spurs: Host Charlotte on Saturday night.
Wizards: Visit Boston on Friday.