The British No 1 needed only 64 minutes to beat the American, a four-time Grand Slam semi-finalist, and set up a clash with ninth seed Roberta Vinci of Italy.
Watson was extending her winning streak against Stephens to four and victory never looked in doubt once she secured her first break of the day.
But Watson is taking things one match at a time despite admitting she is in her best form since winning a couple of ITF tournaments early last year.
“I never think about winning the tournament. It???s a boring answer. You probably want me to say yes, but I???m just focusing on my next match,??? Watson said.
“I???m feeling good and I???m feeling confident, definitely, after these first two matches.
“I had a tough draw in the first match (Watson beat Slovakia’s Magdalena Rybarikova 7-5 6-1) and then Sloane in the second round, so I???m very pleased to get through those matches.
???I thought to myself no matter what happens in the match I???m going to stay aggressive from the first point to the last and I did that today.???