In windy conditions, the No.18-seeded Jankovic was just too consistent for an erratic Hampton, who sent one last shot long - her 29th unforced error of the match - to fall in 62 minutes, 60 62.
"I played very well tonight," Jankovic said. "I started very well from the beginning, hitting my shots and not really allowing Jamie to play her tennis. I didn't really allow her to set up and hit her shots. Because when she's there, she's very dangerous. I was really hitting my down-the-lines, hitting the ball very clean and solid, and just really going after my shots. I'm pretty pleased with my performance."
"It was just one of those days," Hampton said. "Sometimes it happens; unfortunately it happened to me today. Yeah, of course I'm really disappointed. If I were to get back in the match it would have been at the beginning of the second set - I broke her for 1-0, had chances to hold, had chances to break her in the next game as well, and didn't convert. Not great for an attempt at a comeback, really."
The match didn't go on until later in the evening, after the men's match between Stanislas Wawrinka and Richard Gasquet went to five long sets - the players were both asked about the late start.
"Actually it's not easy for anyone," Jankovic said. "Being here all day and waiting for the match, that match lasted like five hours. I had coffee, as well. I was trying to stay awake! I tried my best to keep myself alive, because after waiting a long time it makes you kind of sluggish and makes you sleepy and slow. It's difficult to go out there after that and perform on a high level. I'm happy I could do it."
"The conditions were really slow, and obviously the atmosphere was kind of dead following the great match of Wawrinka and Gasquet," Hampton said. "But that's all part of it. This week was a lot of firsts for me and a lot of new experiences, so that was definitely one of them. I've never played this late, I don't think, even at a Grand Slam. So I'll have to learn and do better next time it happens."
So what does the American take away from her fortnight in Paris? "Last year on the clay I won one match; here I hurt my back as well. So it's been a really good clay court season for me. Made semis of a Premier event and first second week of a Grand Slam. It's been really encouraging, and since Australia I haven't had any problems with my injuries. I'm looking forward to the grass because it suits my game a bit more. And I have nothing to defend until US Open, so it's a good time for me."
As for Jankovic, she moves through to the quarterfinals, her first Grand Slam quarterfinal since right here three years ago, when she would eventually make the semis before falling to Sam Stosur.
"Yeah, it's going to be our first encounter on clay," Jankovic said. "Maria won this tournament last year and has played very well on clay this year and last year. She's a tough opponent. I will go out there and try to play my best tennis and try to perform on a very high level, and we'll see how it goes."