World number two Djokovic needed just 73 minutes to finish off an embarrassingly one-sided 6-1, 6-0, 6-1 mauling of hapless Italian Paolo Lorenzi.
The second-seeded Serb overcame dropping his serve in the opening game to reel off 18 of the next 19 games, firing seven aces as well as 32 winners against 30-year-old Lorenzi, who has never won a Grand Slam match.
"My game was great from start to finish. It was important to be economical with my time on court. I tried to get to the net and stay focussed," said Djokovic, who next faces Brazil's Rogerio Dutra Silva.
Williams, the champion in 1999, 2002 and 2008, and twice a runner-up, was just as ruthless in the concluding match on Arthur Ashe Stadium, sweeping past US compatriot Coco Vandeweghe 6-1, 6-1.
The Wimbledon and Olympic champion, who has 14 Grand Slam titles to her name, next tackles Spain's Maria Jose Martinez Sanchez.
"The conditions were really crazy, but, hey, it's the US Open so you have to be ready for the worst conditions," said Williams, who has won 37 of her last 39 matches on tour.
"I was ready for today and coming here as Olympic champion, I feel so great."
While Djokovic and Williams were enjoying evening strolls, next door on Louis Armstrong court, former world number one and 2009 runner-up Caroline Wozniacki, without a title this year, was crashing to a painful first-round loss.
The Danish eighth seed, watched by golfing superstar boyfriend Rory McIlroy, was beaten by World No. 96 Irina-Camelia Begu 6-2, 6-2.
Wozniacki came into the match with her knee heavily strapped, having picked up an injury at New Haven last week, and she needed more treatment on Tuesday before slipping to defeat.
"I tried and didn't succeed in playing well. There were too many errors. It's frustrating but I will have to move on," said Wozniacki, who made the semi-finals in the last two years.
Andy Roddick, America's last men's major champion when he captured the 2003 US Open title, eased past compatriot and qualifier Rhyne Williams, the World No. 289.
His comfortable 6-3, 6-4, 6-4 win was a gentle way to start his 13th successive US Open appearance, which also comes just two days before his 30th birthday.
Roddick will next face Australia's Bernard Tomic.
Fellow US veteran Venus Williams, the 2000 and 2001 winner, also won an all-American match-up, beating wildcard Bethanie Mattek-Sands 6-3, 6-1.
Williams, playing her 14th consecutive US Open, missed nine months of action with the fatigue-causing Sjogren's Syndrome and came into the tournament ranked at 46.
Victory was a welcome relief after slumping to a first-round loss at Wimbledon this year.
The 32-year-old next faces German sixth seed Angelique Kerber, who knocked her out of the Olympics.
Wimbledon runner-up Agnieszka Radwnaska and former world number one Ana Ivanovic also breezed into the second round as both women look to bury their woeful Flushing Meadows records.
Polish second seed Radwanska and Ivanovic, the 12th-seeded Serb who was French Open champion in 2008, have never got beyond the fourth round in New York but have been quarter-finalists at the other three majors.
Radwanska began her campaign with a 6-1, 6-1 win over Nina Bratchikova with the Russian's challenge undone by 28 unforced errors.
Next up for Radwanska is Spain's Carla Suarez Navarro.
Ivanovic defeated 17-year-old Ukrainian qualifier Elina Svitolina 6-3, 6-2 and goes on to face Sweden's Sofia Arvidsson.
French fifth seed Jo-Wilfried Tsonga, a quarter-finalist in 2011, advanced to the second round by defeating Slovakian qualifier Karol Beck 6-3, 6-1, 7-6 (7/2).
There were also wins for Czech sixth seed Tomas Berdych, who beat Belgium's David Goffin 7-5, 6-3, 6-3, and Spanish 11th seed Nicolas Almagro, who saw off Czech veteran Radek Stepanek 6-4, 6-7 (5/7), 6-3, 6-4.
Canadian 15th seed Milos Ranoic survived a gruelling five-setter to beat Santiago Giraldo 6-3, 4-6, 3-6, 6-4, 6-4, firing 30 aces in the process.
On a bad day for Argentina, 10th seed Juan Monaco surrendered a two-set lead to lose to Spain's Guillermo Garcia-Lopez 3-6, 1-6, 6-4, 7-6 (8/6), 7-6 (7/3).
And former world numer three David Nalbandian pulled out of the tournament, where he was set to face compatriot and 2009 champion Juan Martin del Potro on Wednesday, with a rib injury.