Henman won 6-3, 6-4, to earn a second-round match against another Swede, Thomas Enqvist.
Currently eighth in the Hannover standings, Henman's bid to follow his Davis Cup team-mate, Greg Rusedski, into the second round got off to a solid start, the British No 1 holding his opening service game. He then held two break points on Gustafsson's serve, but the Swede battled through the mini-crisis to level at 1-1.
Henman served with remarkable accuracy during the first set. There were no double-faults or break points from the Oxford-born player and when Gustafsson faltered in the ninth game, Henman responded, grabbing a vital break to lead 5-3.
Gustafsson, ranked 34th in the world, bravely tried to rally as Henman served for the set, but two marginal line-calls went against him and so did the set.
When Gustafsson hit a forehand into the net at break point in the first game of the second set, Henman was in control. However, at 3-2, the Briton endured a setback, losing his service to love. But these days Henman is made of stronger stuff and restored his advantage immediately.
Michael Chang fell to a shock defeat in the first round for the second successive year at the Singapore Open yesterday.
The American No 3 seed and crowd favourite was surprisingly beaten by Michael Kohlmann, a German qualifier, 2-6, 6-3, 6-4. Chang, who lost to his compatriot Jonathan Stark here last year, cruised through the first set, but a break in the seventh game of the second set was enough for Kohlmann to level the match at 1-1.
In the third set it looked as if the German suddenly had all the answers to Chang's strokeplay. Two breaks of serve later Kohlmann was serving for the match at 5-1.
But Chang, fresh from his triumph in the Shanghai Open last week, hung on. He broke Kohlmann's serve and held his own to recover to 5-4. Yet when the German served for the match a second time, he made no mistake.
The No 2 seed, Goran Ivanisevic, sped to a 6-2, 6-1 victory over America's Steve Campbell. He now meets the Australian Mark Woodforde, who overcame South Africa's Marcos Ondruska, 7-6, 6-2.Reuse content