The defending US tennis Open women's champion Sam Stosur of Australia was one of the few players to reach the second round before the rain came on the opening day in New York.
The seventh seed crushed Croatia's Petra Martic 6-1 6-1, while after a two-hour break for the rain, the Olympic champion Andy Murray started slowly against the little-known Russian Alex Bogomolov Jr.
Neither player could hold serve until the fifth game of the opening set when the Scot finally did hold then went on to win the last three games to claim the set 6-2, but Murray struggled again in the second before claiming it 6-4. Murray then wrapped up the match 6-1 in the third.
China's Li Na began her title bid beatig Britain's Heather Watson 6-2 6-3, while Russian Maria Sharapova also went through with a routine 6-2 6-2 win over Hungary's Melinda Czink.
The biggest upset so far was Romanian Sorana Cirstea's 7-6 6-1 elimination of 16th seed Sabine Lisicki of Germany.
Czech qualifier Kristyna Pliskova also knocked out the 18th seeded German Julia Goerges.
Five-times champion and world number one Roger Federer, three-times winner Kim Clijsters and 2006 champion Maria Sharapova are all due on court later.
New Zealander Marina Erakovic is also scheduled to play her first round match against Kristina Mladenovic of France.