Svitolina broke three times en route to an early 5-1 lead and though things tightened up a bit from there, it was too late - Svitolina slid past the No.5-seeded Stephens in straight sets, 64 64.
"I feel more frustration when I'm down 5-1 and I've made like 58 unforced errors in like 12 minutes," Stephens said afterwards. "But after that, you're just like, 'That sucked, but I have to get over it, because I know there are things I can do better.' So it was frustrating, but it's not like I dwelled on it.
"I did well to get it back but it's tough when the other person has momentum and is playing so well."
As for Svitolina, she continues an absolute breakthrough year. Not only has she scored all four of her Top 20 wins so far this year - Svetlana Kuznetsova at the Australian Open, Roberta Vinci in Paris, Eugenie Bouchard at Indian Wells and Stephens here - but this week she became the No.1 teenager.
"I started to believe more in myself that I can compete with players like this, top level, Top 20 and Top 10," Svitolina said afterwards. "I think this belief is the key, and also tactical things like playing more solid from the baseline, trying to go forward and be more aggressive and finishing the points earlier.
"And of course, I'm getting used to life on the tour more. That's the most important thing when you're just coming up from juniors, building the confidence that you can win against these kinds of players."
"Usually I'm at home for at least five or six days to prepare to go from hardcourt to clay, and this time I only had two days to prepare, so it was tough in the beginning," Lisicki said. "But the longer the match went on, the better I started to time the ball and I was making less unforced errors out there.
"It was up and down a bit, but I think I was getting better throughout the match today."
No.3 seed Sara Errani restored more order in the next match on center, though maybe not the way she wanted - Dutch qualifier Kiki Bertens retired with a low back injury after dropping the first set, 6-3.
Other winners early on in the day were No.12 seed Daniela Hantuchova, No.13 seed Elena Vesnina, Peng Shuai and Swiss qualifier Belinda Bencic. Peng had a dramatic win over No.15 seed Madison Keys, originally leading 61 51 - and again 4-1 in the third set - but eventually winning, 61 67(3) 76(4).