The No.11-seeded Williams was the first to advance, though she had it quite a bit tougher, rallying from 5-3 down in the first set and 4-1 down in the second set to beat Chanelle Scheepers, 75 75.
"She was playing so well, but the good thing is that when I get behind, I give even more effort and get even more focused," Williams said. "I've been playing well from behind lately, which is something you have to be able to do to win big matches, because you're not always going to be ahead out there."
Williams is going to need all her fight in her next match - No.6 seed Eugenie Bouchard, who blasted through her second round match in under an hour on Tuesday, is up next for her on Thursday.
Williams beat Bouchard in their only previous meeting, though it was a long, long three-setter.
"Yeah, it'll be a rematch," Bouchard said. "I played her in Tokyo last year, and we had a really tough three set battle. So I'm just looking forward to having another good match. I think she can still play really, really well, and serve really well, so I have to be ready for that when I'm playing her.
"I respect her, of course, but I'm going to believe in myself and believe I can win."
"It was my first match on clay and I didn't know what to expect from myself or how I would play, or what the conditions would be like, especially since it was a night match," Jankovic said afterwards. "Sometimes the ball wasn't coming off my racquet as fast as I wanted it, but I think I did pretty well, and especially that first set was really solid. I was moving very fluid and hitting the ball very clean out there.
"I think Lauren started playing a lot better in the second set, but I was more aggressive too."
Next up for Jankovic is Ajla Tomljanovic, who had the most dramatic win of the day, fighting off four match points in the second set - three serving at 4-5 and another serving 5-6 - and eventually making it past No.16 seed Zhang Shuai in a two-hour, 11-minute thriller out on Court 2, 46 76(4) 63.
Jankovic and Tomljanovic will be playing against each other for the first time.