The 22-year-old Ukrainian, who is the youngest player in the world's top 10 but never a champion on this surface, won 6-2, 5-7, 6-3, recovering from a middle phase when Watson seemed capable of repeating a win she had when they last met on grass, two years ago in Eastbourne.
Svitolina mostly hit the ball hard and flat, much as she did while winning the Italian Open in Rome last month, and only turned to a couple of judicious slices while making the crucial break which got her to 3-1 in the final set.
Otherwise she trusted in her power off the ground to deny the tenacious and intelligent Watson enough time to make court-opening angles and sudden darts to the net.
"It's amazing because I have been struggling a little bit on grass in the last few years," Svitolina smiled.
"I liked the way I handled the game today. There were tight moments as well. She can be a very dangerous player.
"But this has been a good year for me and that means on grass I will be much better (than before). I don't tell myself this is a difficult surface. I play my game, of course with a few small adjustments.
