Venus Williams, shown during a Kastles’ match earlier this month, helped rally Washington to its 25th victory in a row on Saturday night by cruising past another former world No. 1 player, Martina Hingis, of the New York Sportimes in Albany, N.Y. (Matt McClain/For The Washington Post)

Venus Williams helped the Washington Kastles complete the biggest comeback in franchise history on Saturday night for a 21-20 World Team Tennis victory over the New York Sportimes.

The victory was the 25th in a row for the Kastles (9-0) dating to last season.

With Washington trailing, 19-13, with one set remaining, Williams beat Martina Hingis, 5-1, in a singles matchup between former world No. 1 players. Williams went on to win two games in a row, then post a 7-0 win in the supertiebreaker, over Hingis to clinch the victory over the Sportimes (6-3).

“My whole team believed in me,” said Williams, who fended off four match points in overtime. “I’m really glad that I was able to play last, because in singles, you’re in control of it.

“It was like a zone, and everybody on the bench was there for me. I just tried to play from within and it was great to do it for the team.”

After Leander Paes and Bobby Reynolds beat Robert Kendrick and Jesse Witten, 5-4, in men’s doubles, New York moved in front, 9-8, after Kendrick and Hingis teamed for a 5-3 mixed doubles win over Paes and Williams.

Witten’s 5-2 win over Reynolds in men’s singles gave the Sportimes a 14-10 advantage, which stretched to 19-13 after Hingis and Ashley Harkleroad won the women’s doubles match, 5-3, over Williams and Anastasia Rodionova.

Williams and the Kastles host the Kansas City Explorers on Sunday night, after which Williams heads to London for the Olympics.