Former US Open champion Stephens battled back to progress 6-7 (5) 7-5 6-1 in two hours and 50 minutes.
Watson has endured a largely forgettable 2021, winning just seven WTA main draw matches to date, in addition to being eclipsed by the remarkable achievements of fellow Briton Emma Raducanu.
She initially looked well placed to snap a four-match losing streak after claiming a topsy-turvy opening set on a tie-break.
But despite being the higher-ranked player and facing an opponent she had beaten five times in their seven previous meetings, the 29-year-old was unable to complete the job.
World number 73 Stephens – whose own form this calendar year has been inconsistent – secured a crucial break of serve in the 12th game and final game of the second set to level.
The 28-year-old then steamed through the decider, eventually converting her third match point to set up a meeting with compatriot Jessica Pegula in the round of 64.