Kenin dropped her first set 2-6 against unseeded Fiona Ferro before she closed the match 6-2, 6-1 on Monday at Roland Garros. The limited crowd in attendance was in heavy favor of Ferro, who is French.
"Obviously the crowd wasn't for me, so it was obviously tough on me," Kenin told reporters. "I'm happy and super proud of myself."
Kenin will face fellow American Danielle Collins in the quarterfinals on Wednesday in Paris. The winner will battle Petra Kvitova or Laura Siegemund for a spot in the women's singles final.
Kenin, 21, is on a quest to win her second career Grand Slam after she claimed the 2020 Australian Open singles title in February in Melbourne. She had two aces, three double faults, 39 winners and 29 unforced errors in Monday's one-hour, 44-minute victory.
Ferro fired two aces and had four double faults, 21 winners and 25 errors in the loss. Kvitova -- the No. 7 seed -- also advanced with a straight sets win over Zhang Shuai on Monday. Siegemund advanced with a straight-sets win over Paula Badosa.
Unseeded Nadia Podoroska bounced No. 3 Elina Svitolina in a women's quarterfinal match on Tuesday. Collins won her quarterfinal match Monday over Ons Jabeur.
Djokovic headlined the men's singles circuit with a two-hour, 23-minute win over No. 15 seed Karen Khachanov. The 17-time Grand Slam winner will face No. 17 Pablo Carreno Busta on Wednesday for a spot in the semifinals.
Djokovic had two aces, one double fault, 44 winners and 28 unforced errors in his fourth-round match. Khachanov had five aces, four double faults, 31 winners and 31 errors.
Carreno Busta dispatched of Daniel Altmaier in straight sets on Monday. No. 5 Stefanos Tsitsipas and No. 13 Andrey Rublev also advanced with fourth-round victories. They'll also match up on Wednesday at Roland Garros.