The 22-year-old Briton opened by breaking the twice French and Australian Open champion, but faltered in the final set, falling behind 4-0 and eventually succumbing in two hours and 24 minutes.
"The first two sets were very close, but in the third I got going early and I played solidly. I'm happy with that," said Courier, who joined the ATP Tour in 1988.
"I think we both played admirably, especially bearing in mind the conditions. In the end, I bottom-lined it and came up with the last point."
It was the first appearance in a Tour event final for Henman, who reached the Wimbledon quarter-finals last year and is starting his fourth year on the tour.
Courier claimed the first set with a break in the 12th game, but Henman levelled the match by winning the second set in the tie-break after a break of serves each.
It was then that the 26-year-old American's experience began to show. He earned two breaks to open the final set, taking advantage as Henman gradually lost control and committed a series of sloppy unforced errors.
Courier completed the victory and earned the $84,000 (pounds 56,000) winner's purse when Henman carelessly netted a return.
Courier, who became the world No 1 in 1992, will climb to 15th when the tour releases the world ranking today, which should earn him a seeded place at the Australian Open, which starts a week today.
Despite the defeat, Henman could rise above his career high of 25, but the British No 1 said that there were areas of his game that needed work.
"My intensity level dropped in the final set. I should have been trying to step it up, but I went in the opposite direction," he said. "I have to be harder on myself."
"You need mental toughness to play good points. The third set happened so quickly and you can't afford to let it happen against a player of Jim's class."
Mark Philippoussis was forced to pull out of the Sydney International event yesterday because of tendinitis in his right forearm. The Australian hit with the top seed Goran Ivanisevic for 30 minutes before the injury forced him off court.
The tournament director, Barry Masters, said that Philippoussis, who ended last year ranked 30th, was advised by doctors not to hit balls for the rest of the week so he can recover for next week's Australian Open.
The doubles specialist Todd Woodbridge won the second singles title of his career yesterday with a crushing 6-2, 6-1 defeat of his Australian compatriot Scott Draper in the final of the Australian Hardcourt Championship in Sydney.Reuse content