The 27-year-old Belgian second seed will play Australia's Sally Peers, who defeated Aleksandra Wozniak of Canada 6-1, 6-0, for a place in the third round.
A year on from her stunning win at Flushing Meadows when she stepped out of retirement and motherhood to lift her second Grand Slam title, Clijsters was again in a dominant mood on the Arthur Ashe Center Court.
She sped through an uneven first set in just 18 minutes, but allowed the 30-year-old Arn, ranked 104th in the world, to play her way back into the match with two breaks of serve to lead 4-0 in the second set.
Whether it was over-confidence after the first set romp, lethargy brought on by the sultry conditions, or the lingering effects of the right thigh injury that hampered her in Montreal, Clijsters looked suddenly very uncomfortable.
She battled back to 4-3 down, but Arn served for the set two games later only to be broken by a resurgent Clijsters.
The Belgian held for a 6-5 lead and then broke Arn again to move through in 62 minutes.
There was a more comfortable winning start for this year's surprise French Open champion, Francesca Schiavone of Italy, who coasted past Japan's Ayumi Morita 6-1, 6-0 in just 58 minutes.
The 30-year-old Schiavone played the tennis of her lifetime to win in Paris in June, but since then she has struggled to reproduce that kind of form and intensity.
That was only normal, she insisted.
"When you try to reach in the top of the mountain, then you can't go more up. So you have to go down and come back up again.
"I think I am doing this one. And when it's time to come back up again, I will do it. I'm working to do it." Among others to go through early on were Russia's Elena Dementieva, the runner-up here in 2004 when she also reached the final of the French Open. The 12th seed had too much firepower for Olga Govortsova of Belarus, winning 6-1, 6-2.
Elena Baltacha meanwhile gave a much needed boost to British tennis by defeating Petra Martic of Croatia, who beat her at Wimbledon, 6-2, 6-2, while Melanie Oudin, a huge crowd favorite from Marietta, Georgia, needed just 56 minutes to beat Olga Savchuk of Ukraine 6-3, 6-0.
If anything, Schiavone seems to be having fun in the spotlight. Asked why she's a fan favorite, she playfully replied, "I attract them because I'm beautiful." Schiavone acknowledged that maybe she's a bit more motivated at a Grand Slam than at other tournaments. She was pleased that her first-round match was in the grandstand - a year ago, she was relegated to an outer court.
"I like to do it, because adrenaline is coming up and I enjoy much more than play in faraway court," she said with a laugh. "Maybe because I am 30 years old and now I want to enjoy with people."
The 43rd-ranked Oudin won the last nine games against Savchuk, a 143rd-ranked qualifier. Oudin's success last year earned her the opening match in Ashe, where the sparse crowd gave her a warm ovation when she took the court a little after 11 a.m.
Oudin snapped a four-match losing streak and won for only the fifth time in her past 18 matches. A year ago, she became the darling of the tournament, upsetting Maria Sharapova and Elena Dementieva en route to becoming the youngest US Open quarterfinalist since Serena Williams in 1999.
Schiavone, seeded No. 6, had been just 3-6 since winning at Roland Garros. She lost in the first round at Wimbledon and dropped her opening match at three other tournaments. Her only three victories came against opponents outside the top 65.
Schiavone had no trouble against the 83rd-ranked Morita, facing just one break point and hitting 28 winners.
Russia's Elena Dementieva, the No. 12 seed, also advanced easily, beating Olga Govortsova of Belarus 6-1, 6-2.
Fellow Russian Nikolay Davydenko, the No. 6 seed on the men's side, beat American Michael Russell 6-4, 6-1, 6-3.
The Russian, twice a semifinalist in New York but still making his way back after a wrist injury this year, recovered from a slow start to cruise through in two hours, 21 minutes.
