Venus Williams gained revenge for her Wimbledon final defeat by Garbiñe Muguruza when the American advanced to the last four of the WTA Finals with a gutsy 7-5, 6-4 victory over the Spanish world No2.

Both players knew a win would secure a passage to the semi-finals as they held identical 1-1 records in White Group at the season-ending event but the 37-year-old was stronger on the key points and moved brilliantly around the court to progress.

Muguruza had brushed aside Williams to claim her second grand slam title in July but any hopes she had of repeating the feat were snuffed out by a resolute opponent, who simply refused to buckle in the tense Singapore Indoor Stadium encounter.

“I played an amazing opponent who has had an amazing year so I was so happy to win the last point,” Williams said.

The victory enabled Williams, who won this event in 2008, to advance along with the pool winner, Karolina Pliskova, who won her first two matches but ended round-robin play with a 6-3, 6-1 defeat by Jelena Ostapenko earlier on Thursday.

Williams added: “It’s not easy out here, you have to play every point well or you end up losing the game. I had some great coaching going into my match and I hope I can win some more.

Ostapenko ended her maiden WTA Finals campaign on a winning note with a surprisingly easy victory over a subdued Pliskova, the Latvian saving her best until last after she was eliminated earlier in the week.

Pliskova, the world No3, won her opening two matches against Williams and Muguruza to book a semi-final berth but the Czech was outgunned by an inspired French Open champion in 66 minutes. Ostapenko had battled hard in her opening matches to no avail, especially in a gruelling three-set loss to Williams, but she served brilliantly against Pliskova and found the corners with her booming forehand to end her season with a win.

Ostapenko said: “Yes, I lost my earlier two matches but it’s my first time here and I am just happy to finish my season here, in the top eight, especially with a win at the end.”

Caroline Wozniacki has already advanced from the Red Group with one round of matches remaining, while Simona Halep, Caroline Garcia and Elina Svitolina can all still qualify alongside the Dane when play concludes in that pool on Friday.