The British No 1 arrived in Sydney in the early hours before his first match against Renzo Furlan, having taken three separate flights from the Middle East.
He was broken in the first game but rallied to break the Italian in the next and went on to secure a 6-3, 6-4 victory just before midnight.
Afterwards Henman was relieved to have finally got his preparations for the Australian Open under way following a nightmare trip from Doha and a long delay for rain.
"I just tried to forget what I had been through in the last 24 hours,'' the world No 24 said. "When you are confident and hitting the ball well you don't think about too much out on the court.
"My concerns before the match were mental and physical. I wasn't sure how I would feel and how focused I would be. Overall I think it was a good performance. Tennis-wise I hit the ball well."
The 22-year-old from Oxford was particularly glad to have bounced back after losing the first game to the Italian, ranked 15 places below him.
He said: "In the first game I had 40-15 but then didn't play particularly well. It was a bad start to the match. But once I broke back in the second game of the match I felt pretty comfortable. I wanted to keep the momentum going this week."
The victory was a superb achievement by Henman following his tortuous journey to Sydney after his defeat by Jim Courier in the final of the Qatar Open in Doha. After finishing the match at around 7pm local time, he went directly to the airport to catch a 9pm flight, firstly to Abu Dhabi and then on to Bangkok.
He then checked into a hotel for four hours and managed to fit in a work- out with coach David Felgate before catching a British Airways flight to Sydney, landing at 6.30am local time.
After just a few hours sleep Henman then went for a warm-up but was frustrated by heavy rain. With the first-round matches delayed he eventually got on court at 10pm and wrapped up victory just before midnight.
Henman was due to face the former French Open champion Sergi Bruguera in the second round today after the Spaniard defeated his compatriot Felix Mantilla.
Spain's Arantxa Sanchez Vicario was the most prominent victim of the day yesterday as the seeds tumbled out of the tournament. Half of the 16 men's and women's seeds lost first-round matches including the men's No 2 seed, Wayne Ferreira of South Africa, beaten 2-6, 6-0, 6-3 by Spain's Carlos Moya.
Sanchez Vicario, the world No 3 and top seed in the women's draw, lost 6-3, 6-3 to American Amy Frazier, ranked 33, in a match delayed by rain and hit by high summer winds.
Jennifer Capriati defeated her fellow American Chanda Rubin and Yayuk Basuki of Indonesia beat Mary Pierce in straight sets.
Monica Seles, winner of the Australian Open four times, will be unable to defend her title next week because of a broken finger. Seles broke her right ring finger in two places while warming up for an exhibition tournament last month and has been unable to play since 4 December. The French No 1, Cedric Pioline, has also withdrawn because of back trouble.
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