The Italian from Taranto, ranked at number 15 in the world, wrapped up a comfortable straight-sets victory over the British number three, who only qualified for the tournament as a lucky loser.
Vinci, the Luxembourg champion in 2010, won in 64 minutes and will next take on either ninth seed Mona Barthel of Germany or American Venus Williams in the last eight.
Second seed Julia Goerges was dumped out of the tournament 6-4 6-2 by Monica Niculescu.
The Romanian is now 2-2 in matches played against her German opponent, with Georges having won the first match between them for four years recently in Tokyo.
Third seed Jelena Jankovic suffered a catastrophic final set as she was knocked out 7-5 6-0 by Andrea Petkovic. The nervous Serbian, who served five double faults, was competitive in the first set as she broke the German twice but was broken three times herself.
Unseeded American star Venus Williams went through in straight sets 7-6(4) 6-4 against ninth seed Mona Barthel of Germany.
In the WTA Moscow event, top seed Samantha Stosur survived a scare against Alize Cornet before beating the Frenchwoman 7-6 7-5.
On the last match on centre court, 43rd-ranked Cornet served for the first set but failed to take her chances against the 2011 US Open winner, losing a tiebreak 8-6.
Cornet also led 5-4 in the second, and after wasting three set points ran out of gas as Australian Stosur secured a hard-earned victory just before midnight. The match lasted two hours and a half and featured 15 breaks of serve and 24 break chances.
Fourth seed Serbian Ana Ivanovic booked her spot in the last eight with a routine 6-1 6-4 win over Russian qualifier Valeria Solovieva.
"I think she looked nervous, especially in the first set, because it was probably her first big match," former world number one Ivanovic said.
Ivanovic next meets 158th-ranked compatriot Vesna Dolonc.
Moscow-born Dolonc, who took Serbian citizenship last year, crushed Romanian Simona Halep 6-1 6-0 to reach her first quarter-final on the WTA Tour this year.
WTA Luxembourg results
Monica Niculescu (Romania) beat 2-Julia Goerges (Germany) 6-4 6-2
Venus Williams (U.S.) beat 9-Mona Barthel (Germany) 7-6(4) 6-4
Andrea Petkovic (Germany) beat 3-Jelena Jankovic (Serbia) 7-5 6-0
1-Roberta Vinci (Italy) beat Anne Keothavong (Britain) 6-4 6-1
Ksenia Pervak (Kazakhstan) beat 6-Sorana Cirstea (Romania) 7-6(4) 6-1
Daniela Hantuchova (Slovakia) beat Kirsten Flipkens (Belgium) 6-4 4-6 6-2
WTA Moscow results
1-Samantha Stosur (Australia) beat Alize Cornet (France) 7-6(6) 7-5
4-Ana Ivanovic (Serbia) beat Valeria Solovieva 6-1 6-4
7-Maria Kirilenko (Russia) beat Yaroslava Shvedova (Kazakhstan) 7-5 6-4
Vesna Dolonc (Serbia) beat Simona Halep (Romania) 6-1 6-0
- Mona Barthel
- Venus Williams
- Alize Cornet
- Monica Niculescu