The world number 83, who entered the tournament’s main draw as a ‘lucky loser’, defeated the WTA Fes champion in a convincing performance.
Keothavong now has a 3-0 head-to-head record over the Dutchwoman, having beaten the world number 60 twice last year.
The top seed in Luxembourg is Roberta Vinci of Italy.
Marion Bartoli was sent crashing out of the Kremlin Cup in Moscow as Sofia Arvidsson of Sweden won 6-3 6-0 to stun the second seed.
Bartoli, who had a bye in the first round, looked out of sorts on the hard indoor surface, committing 10 double faults and winning only 50 per cent of her first serves.
The world number 10 showed little resistance after losing the opening set and conceded the match with a half-hearted forehand into the tramlines after 75 minutes.
"Mentally I was fine but my body was just not reacting. I was feeling tired and exhausted and, of course, the surface was very slow so it didn't help my game," Bartoli said.
"It was very difficult for me to beat her on this kind of surface because she likes to have time to get the ball back and she had all the time in the world here."
The French player is challenging with Samantha Stosur for ninth place in the Race to WTA Championships – the first alternate if a top-eight player drops out.
In the quarter-finals, 46th-ranked Arvidsson, who beat Bartoli for the fifth time in seven matches, faces seventh seed Maria Kirilenko of Russia or unseeded Kazakh Yaroslava Shvedova.
Kirilenko beat compatriot Elena Vesnina 7-5 6-1 in the first round, while Shvedova dismissed Russian Anastasia Pavlyuchenkova 6-2 6-2.
Former world number one Caroline Wozniacki reached the quarter-finals after easing past Poland's Urszula Radwanska 6-1 6-3.
The third seed from Denmark wasted five match points on her serve in the eighth game of the second set before finally ending the 29th-ranked Radwanska's resistance a game later.
World number 11 Wozniacki now takes on last year's winner Dominika Cibulkova after the fifth-seeded Slovak beat Tsvetana Pironkova of Bulgaria 6-2 6-3.
Czech Klara Zakopalova became the first woman to reach the last eight of the annual indoor tournament after upsetting eighth-seeded compatriot Lucie Safarova 6-4 6-4.
Australian top seed Stosur begins her action on Thursday against France's Alize Cornet.
Although none of the WTA Championship qualifiers are competing in Moscow this year, the Kremlin Cup still has a fine field, featuring three former Grand Slam champions, two former world number ones and the defending champion, Dominika Cibulkova.
WTA Moscow results
3-Caroline Wozniacki (Denmark) beat Urszula Radwanska (Poland) 6-1 6-3
5-Dominika Cibulkova (Slovakia) beat Tsvetana Pironkova (Bulgaria) 6-2 6-3
Sofia Arvidsson (Sweden) beat 2-Marion Bartoli (France) 6-3 6-0
Klara Zakopalova (Czech Republic) beat 8-Lucie Safarova (Czech Republic) 6-4 6-4
7-Maria Kirilenko (Russia) beat Elena Vesnina (Russia) 7-5 6-1
Valeria Solovieva (Russia) beat Elina Svitolina (Ukraine) 6-4 6-2
WTA Luxembourg results
Lucie Hradecka (Czech Republic) beat Annika Beck (Germany) 6-1 6-1
Lourdes Dominguez Lino (Spain) beat Magdalena Rybarikova (Slovakia) 6-2 6-3
Andrea Petkovic (Germany) beat Garbine Muguruza Blanco (Spain) 4-6 6-2 6-1
Ksenia Pervak (Kazakhstan) beat Vera Dushevina (Russia) 6-3 7-6(2)
Anne Keothavong (Britain) beat Kiki Bertens (Netherlands) 6-2 6-2
Daniela Hantuchova (Slovakia) beat Arantxa Rus (Netherlands) 3-6 6-4 6-1
- Sofia Arvidsson