Stephens, a Florida native and the 2018 Miami Open champion, converted four of her eight breakpoint chances against Kerber and dropped serve once in the 70-minute match.
"I came out with a gameplan, I was very clear with that, and I didn't really deviate from that," Stephens said during her on-court interview.
"I just tried to play the best I could and give the best effort I could and I'm happy to be through with the win."
Up next for the 2017 US Open champion, who fell in the third round at Indian Wells last week, will be a clash with Romania's Sorana Cirstea.
World number 41 Stephens was barely tested in the first set which she wrapped up in style with her second break of the frame, this one coming at love.
Kerber, a three-times Grand Slam winner who returned to the tour in January after an 18-month maternity break, was looking to build on her fourth-round showing at Indian Wells.
She appeared more comfortable early in the second set but was ultimately undone by a rash of errors.
Stephens took advantage and consolidated a break for a 5-2 lead and then went on to serve out the match with a routine hold that she punctuated with a forehand to the open court.
With the win, Stephens improved to 6-2 in head-to-bead meetings with Kerber.
