(CNN) -- Second seed Serena Williams stormed into the semifinals of the season-ending WTA Championships in Doha, while sister and defending champion Venus kept her slim hopes alive.
Serena, who will end the year as world No. 1 after Dinara Safina pulled out of the tournament with a back injury on Wednesday, won her third successive match in the Maroon Group with a 6-2 6-4 demolition of Elena Dementieva on Thursday.
She defeated Venus the previous day, but her win over the Russian gave her older sibling hope of progressing in the stifling heat of Qatar.
Serena trailed 2-1 after an early break, but then after a marathon seven-deuce game she won five in a row to take out the first set, and had few problems in raising her game when necessary in the second.
The 28-year-old made just 13 unforced errors to her opponent's 20, and made 28 winners to Olympic champion Dementieva's 20.
"It was definitely a match I had to be really focused for, because she's a really good player," Serena told the WTA Tour's official Web site.
"She's one of those late bloomers where she tends to get better and better and better as every year goes on in her career. I was probably playing the most fit girl on tour."
Venus Williams lost her first two matches in three-set affairs, and was taken to a decider by Svetlana Kuznetsova for the first time in their eight career encounters before prevailing 6-2 6-7 (3-7) 6-4 in two and a half hours.
The American's hopes of reaching the last four now depend on Kuznetsova beating her fellow Russian Dementieva on Friday so all three players are left with one victory, with the player with the best record going through.
Venus struggled with her serve in the first set, making five double-faults, but still won it easily as both players went for their shots.
She was broken in the seventh game of the second set, but pegged it back to 5-5 before losing her way in the tie-break.
French Open champion Kuznetsova visibly tired in the decider, as both players struggled to hold serve, but she saved two match-points before hitting a forehand wide.
In the White Group, fourth seed Caroline Wozniacki claimed her second victory after a marathon clash with Vera Zvonareva, who was brought in after her follow Russian Safina's withdrawal.
The Dane triumphed 6-0 6-7 (3-7) 6-4 in a match lasting two hours and 48 minutes which saw both players require treatment -- with Wozniacki collapsing on court with spasms of cramp just two points from victory, incurring a time violation.
Sapped by the humid conditions, she was playing her second near-three-hour match in successive days, and had one of her legs heavily strapped.
Zvonareva battled back after being understandably rusty in the opening set, winning the second set despite needing lengthy treatment to stem a nosebleed.
U.S. Open runner-up Wozniacki, at 19 the youngest player in the eight-player field, blew a 3-1 lead but showed great resilience to give herself a great chance of reaching the last four in her first appearance at the event.
Her final match is against former world No. 1 Jelena Jankovic, who lost to Azarenka but picked up a win when Safina pulled out early in their match.