By Julian Linden
Vera Zvonareva also breezed through, reaching the last four in New York for the first time, but the trio were more relieved than excited after a day when gale force winds turned the last grand slam of the season into a lottery.
"This felt like playing in a hurricane," Wozniacki said after beating unseeded Slovakian Dominika Cibulkova 6-2 7-5. "It was just about surviving."
The wind inside Arthur Ashe Stadium was blowing so hard that hitting winners almost became a secondary consideration.
The players were repeatedly having to re-toss after gusts blew the ball out of their reach when they were serving. Just landing the ball on the court became an achievement in itself.
"These are the worst conditions at this tournament," Djokovic grumbled after his 7-6 6-1 6-2 victory over Frenchman Gael Monfils. "I don't think the crowd enjoyed the tennis too much."
Zvonareva was almost apologetic after her 6-3 7-5 win over Estonia's Kaia Kanepi that featured 11 service breaks and 88 unforced errors.
"We both were trying our best out there," she explained.
The wild weather lent itself to some comical moments but for the tennis purists, it was a day to forget. The only consolation was that Mother Nature did not claim any victims and the three favorites all won easily.
The acrobatic Monfils provided Djokovic with some worrying moments when he grabbed an early service break but the world number three was able to break back and win the first set tiebreaker before running away with the match.
His next opponent will either be Roger Federer, who beat him in the 2007 final and the semi-finals each of the past two years, or Sweden's Robin Soderling, runner-up at the French Open the last two years. World number one Rafa Nadal is lurking on the opposite of the draw.
"I like playing under the radar sometimes. It releases the pressure on myself," Djokovic said.
After reaching the final 12 months ago and starting this year's championship as the top seed, Wozniacki automatically forfeited any hope she had of quietly sneaking through.
"I'm really competitive," she said. "I really don't like losing."
Zvonareva has been one of the most improved players on the women's tour this year and is Russia's highest-ranked player.
She made her first grand slam final at Wimbledon in July and is through to her first semi-final at Flushing Meadows.
"I guess I'm improving," she said. "I've been playing for a while, but I'm still out there and still working hard."