Konta, the British No 1 and 11th seed, moved into the third round of the BNP Paribas Open with a 6-4 6-4 win on Stadium 1.
Their only previous meeting came four years ago in a second-tier event in Barnstaple which saw Watson retire injured after losing the first four games.
This time it reached a proper conclusion and Konta, ranked 97 places above her opponent, made her quality tell despite some tough moments.