Defending champion Samantha Stosur was defeated by top seed Victoria Azarenka in one of just two matches completed before downpours ended the action at Flushing Meadows.
US Open: Organisers face matches backlog as heavy rain suspends play
It marked the seventh year in a row that rain has caused major disruptions at the season's final Grand Slam event on the Flushing Meadows hardcourts and raised fears of a rain-delayed Monday men's finish for the fifth year in a row.
In the only completed women's match, top seed Victoria Azarenka of Belarus shook off a 75-minute rain delay after just 11 minutes to reach a semi-final by beating defending champion Samantha Stosur of Australia 6-1, 4-6, 7-6 (7/5).
"It's never pleasant to stop the momentum but it was the same for both of us," Azarenka said.
The only men's match to be completed saw Spanish fourth seed David Ferrer advance to the quarter-finals with a 7-5, 7-6 (7/2), 6-4 win over France's Richard Gasquet.
"The rain made it very difficult," said Ferrer. "But the fans have been great and I wanted to win it for them."
Four unfinished singles matches were suspended until Wednesday, with French 11th seed Marion Bartoli leading Russian third seed Sharapova 4-0 until being rescued by the rain that forced them off the court at Arthur Ashe Stadium.
On the men's side, defending champion Djokovic, the second seed from Serbia, managed a break for a 2-0 lead over Swiss 18th seed Stanislas Wawrinka in the 10 minutes they were on the court before showers struck.
Djokovic, or whoever reaches the final from his half of the draw except Ferrer, might have to play four of the final five days of the event, provided weather allows for an on-time men's finish for the first time since 2007.
Rain, however, is in the forecast until the weekend.
Serbian eighth seed Janko Tipsarevic seized a 5-2 lead on German 19th seed Philipp Kohlschreiber before the last deluge shut down play at about 9pm, 30 minutes before officials suspended resumption to Wednesday.
That ensured one more day in the career of Andy Roddick, the 2003 US Open champion who said last week this would be the final event before he retires.
US 20th seed Roddick won the first point of a first-set tiebreaker against Argentina's seventh-seeded Juan Martín del Potro, the 2009 US Open winner, before their match was halted.
In all, there were four rain delays for the day, the last for 30 minutes and the one before it for three hours.
Early stoppages of about 75 and 88 minutes kept the court-drying towel crews on outer courts and electronic drying machines at Ashe Stadium busy.
With retractable roof facilities at the Australian Open and Wimbledon, and one planned to open at the French Open by 2017, the US Open is the only Grand Slam event not to have any covered court or plans to create one.
That made for scheduling chaos for broadcasters and left 40,000 spectators on the day with more time waiting in the rain than watching matches.
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