Around four hours of play were washed out, forcing tournament officials to drastically revise the schedule so Andy Murray could finally begin his title defence.
In the women's draw, Poland's Agnieszka Radwanska, the third seed, easily defeated Maria-Teresa Torro-Flor of Spain 6-0 7-5 while China's Li Na beat the rain to dispose of Sweden's Sofia Arvidsson 6-2 6-2.
"I was a little bit happy because at least I'm done for my job today," said Li.
Only five matches were completed in the morning before the rain arrived, sending players and spectators scampering for cover.
Players made a brief return to the courts when the drizzle stopped midway through the afternoon but another downpour saw them retreat to the locker room, forcing organisers to cancel 28 matches.
Serena was due to play Galina Voskoboeva on centre court but their second round meeting was among the matches postponed in a bid to complete the men's first round.
Because of the unique scheduling at the US Open, where the men's first round is played over three days, Murray was not scheduled to play his opening match until Wednesday night.
His match against Frenchman Michael Llodra did not begin until almost 10 p.m. local time but at least he avoided the prospect of starting his defence on day four.
New York's fickle weather has been a major talking point at Flushing Meadows for years with each of the last five men's finals spilling into a third week because of rain delays.
The problem has been exacerbated because of the tournament's controversial scheduling.
Apart from playing the men's first round over three days, the U.S. Open was previously the only Grand Slam where both singles semi-finals and finals were played on successive days, leaving no room for catch-up if rain falls on the last weekend.
Tournament organisers tweaked the schedule this year to provide a day off between the semi-finals and final, but remain powerless to combat Mother Nature.
The US Open is the only Grand Slam where the main stadium is not covered by a roof. For years, US Tennis Association officials balked at the idea of building one because of the cost of covering Arthur Ashe Stadium, the largest tennis stadium in the world.
But they have finally relented, announcing two weeks ago that they would commence a massive renovation program, which would include a roof, but not until 2016 at the earliest.