The American, champion here in 1998, beat Italian Maria Elena Camerin 6-2, 6-4 in the first match of the evening session at Flushing Meadows in New York.
"It felt good, I managed to get through relatively easily," Davenport said after her second-round victory.
Earlier, Wimbledon men's champion Federer opened his U.S. Open campaign with a first-round win, Argentine Jose Acasuso retiring because of cramps with the Swiss player leading 5-7, 6-3, 6-3, 2-0.
Women's world number one Clijsters thrashed American Laura Granville 6-1, 6-1 in 49 minutes.
Davenport, a former world number one and three-times Grand Slam winner, has had her last 18 months disrupted by knee surgery and a more recent foot injury.
But despite appearing a little hesitant on Arthur Ashe Court, the 27-year-old was happy enough with her progress.
"I wasn't on top of the ball as much as I would have liked," said Davenport, who has had a cortisone pain-killing injection in her foot.
MORE SURGERY
"But the foot felt fine. Hopefully it will improve every day so I can feel more confident with it. That's very important...now I have to think more about playing the type of tennis that is going to win the tournament."
Davenport, who will undergo more surgery after the U.S. Open, said the thought of curtailing her career because of fitness concerns was not on the agenda.
She said: "I was really frustrated (after this year's Wimbledon) with having another injury, another lay-off.
"It takes its toll mentally but I'm happy I stuck around this summer. It's given me motivation to come back and see what happens next year."
Federer, the second seed, swiftly recovered from a stuttering start to impose himself on Acasuso.
The Swiss would have expected minimal resistance from the 75th-ranked Acasuso after the claycourter had won only one match since April and suffered first-round exits in six of seven previous events.
The Argentine offered plenty of fight on his way to taking the opening set but there was never a hint of panic from the stylish Federer.
"I was already winning at that stage," Federer said after Acasuso's retirement.
His victim in last month's Wimbledon final, Mark Philippoussis, was also in control. The 20th-seeded Australian beat Serb Janko Tipsarevic 6-2, 7-6, 6-4.
CLIJSTERS SUBLIME
Belgian Clijsters, yet to win a Grand Slam crown, was sublime against Granville and was joined in the third round by ninth seed Daniela Hantuchova, who survived a late scare against Ukrainian Julia Vakulenko to win 6-0, 7-6.
"I lost a little bit of my rhythm in the second set so I am definitely relieved," said Hantuchova.
It was not a victory without drama, the emotionally frail Slovak almost bursting into tears when she missed a match point in the 10th game of the second set.
But Hantuchova quickly pulled herself together and will next meet Thai Tamarine Tanasugarn, who ousted 18th-seeded Swiss Patty Schnyder 6-4, 6-3.
Amelie Mauresmo also advanced, the fifth seed trouncing fellow Frenchwoman Stephanie Cohen Aloro 6-2, 6-2.
After skipping Wimbledon through injury, Mauresmo said she was finally healthy and looking forward to a successful run at Flushing Meadows.
"I am feeling more and more competitive out there, that's what is important," she said. "No more problems with my back or whatever...so far so good."
