Tsurenko, the only unseeded woman to reach this stage of the tournament, will be playing in her first Grand Slam quarter-final when she kicks off Wednesday's action on what is expected to be another steamy day in NY.
Millman kept up the pressure even when Djokovic tried to shorten points with drop shots.
Kei Nishikori outlasted Marin Cilic in a rematch of the 2014 U.S. Open final, moving into the semifinals with a 2-6, 6-4, 7-6 (5), 4-6, 6-4 victory. "This has been definitely the toughest US Open in the last 10 years that I have played in in terms of conditions".
"Very tested", Djokovic said. "I was not feeling well", she said.
Keys won all 10 of her service games, saving the only two break points she faced.
"I was just trying to hang in there and try to find a way to win the match".
The 13-time Grand Slam champion sealed the victory after 2 hours and 48 minutes.
But they also underscore a growing problem: increasing nighttime temperatures.Under climate change, overall temperatures are rising - 2018 is on track to be the fourth-warmest year on record - but the warming is not happening evenly. That break seemed to give Djokovic some much-needed rest and he sat down on his sideline bench without a shirt on and cooled off.
Tropical Storm Gordon tracks toward central Gulf coast; landfall expected tonight
As much as 8 inches (20 centimetres) of rain could fall in some parts of the Gulf states through late Thursday. Hurricane warnings are posted for Alabama and MS with Tropical Storm Warnings for parts of eastern Louisiana.
Brett Kavanaugh Supreme Court confirmation hearings begin
Democrats have protested the White House's withholding of 100,000 pages of documents related to his years in the Bush White House. The Constitution establishes me as an independent judge bound to follow the law as written, the precedents of the Supreme Court".
Tropical Storm Gordon lashing Panhandle, expected to become hurricane before landfall
As of early Wednesday, Gordon was about 20 miles northwest of Hattiesburg, Mississippi, with sustained winds of 40 mph. Communities along the coast provided sand and bags, and many hustled to protect their properties ahead of the storm.
Osaka wasn't born when compatriot Kimiko Date made the Wimbledon semi-finals in 1996 but now the 20-year-old has the opportunity to go one better by reaching a maiden Grand Slam final.
Djokovic was an nearly unbackable favourite against the Queenslander despite his heroics the previous round against Roger Federer - with a Millman victory paying anywhere between $9 and $14. He fended off seven break points but couldn't stop Djokovic from converting on the eighth to take the two-sets to one lead. "I'd play in a swimming pool if I got to play a quarter-final every week at a Grand Slam".
Keys, the 2017 runner-up, leads Osaka 3-0 in career meetings including the third round at the US Open in 2016 when she battled back from 1-5 in the final set to triumph.
Tsurenko labored in the heat during her fourth-round victory over Marketa Vondrousova, having her temperature and blood checked during a medical timeout in the first set and almost quitting when she trailed early in the second.
"Especially the top players, they always try to set their own form, so to say, around the Grand Slams because that's where they want to play their best".
Djokovic will meet Japan's Kei Nishikori in the last four having already swatted aside Hungary's Marton Fucsovics, American Tennys Sandgren, Richard Gasquet of France and the Portuguese Joao Sousa.
In fact Cilic has won all three of their clashes at the US Open - beating Nishikori in the second round in 2010 and in the third round in 2012. Naomi Osaka took her place in the semifinal with a win over Lesia Tsurenko in straight sets on Wednesday.
Still in search of her first Grand Slam title, the Keys reached her third semifinal in the past five majors by using her big-strike game built on serves and forehands to overpower No. 30 Carla Suarez Navarro of Spain 6-4, 6-3.