Playing her first match since a first-round defeat at Wimbledon last month, the British number two came from a set down to beat qualifier Alexandra Mueller 6-7 (5/7) 6-4 6-3 in two hours and 10 minutes.
Watson blew a mini-break lead as she lost the first set on a tie-break but she put that setback behind her by levelling the match in the second.
She broke her American opponent's serve in the third game of the decider only for the world number 499 to hit back immediately.
However, from 2-3 down Watson reeled off four straight games to seal her place in the second round.
She finished with 14 aces on the slick hardcourts of the US capital.
The 21-year-old will next face fourth seed Alize Cornet after the Frenchwoman defeated Yanina Wickmayer 6-1 6-3.