Henman had little difficulty in taking the first set, but his opponent was sharper in the second, which went to a tie-break as the British No 1 lost his fluency. But he got through this crisis to take the tie-break comfortably and progress into the last four of a tournament he now has every chance of winning.
Henman, who has never reached an ATP tour final, will now play diminutive left-handed Morrocan Hicham Arazi, 23, in the semi-final. Arazi beat Magnus Larsson of Sweden 7-6, 7-6.
The other semi-final will see the American former world No 1, Jim Courier, take on Spain's Sergi Bruguera, twice winner of the French Open.
Henman, looking to improve his world ranking of 29, broke Gustafsson in the fourth game of the first set to love with some excellent groundstrokes.
In a match played mostly from the baseline, Henman at once started to dominate an opponent he beat in straight sets on his fine run to the quarter- finals at Wimbledon last summer.
Henman had clearly taken confidence from the last round when he eased past Egypt's Tamer El Sawy on New Year's Day 6-3, 6-2.
The seventh game was perhaps the key to the opening set. Henman, under real pressure on his own serve, was taken to deuce, but the Briton held his nerve to move into a 5-2 lead.
Yet in the second, Henman the highest-ranked player not seeded for this event battled to keep his momentum against fifth-seeded Gustafsson as the Swede, celebrating his 30th birthday, launched an impressive comeback.
Gustafsson had four break points in an epic fourth game of the second set yet Henman, struggling with his first serve, did enough to win through. But the Swede refused to concede defeat, punishing some loose play and some ill-judged drop shots from his opponent to earn three separate set points at 6-5.
Henman, however, saved each of them to take the second set into a tie- break, and he at once moved into a 4-1 lead as Gustafsson lost his way and the match.
Courier extended his stranglehold over Thomas Muster to seven successive wins. Courier's 6-3, 7-5 quarter-final victory extended a sequence stretching back to the 1992 Australian Open.
Courier, who has won four Grand Slam titles, thrived in the windy conditions while Muster said he had not fully recovered from a marathon second round win over Christian Ruud on Thursday night.
"I'm used to playing in a stiff breeze so it doesn't worry me," Courier said. Muster broke Courier in the first game but the American returned the compliment and broke decisively in the eighth game. Courier broke through again in the 11th game of the second set before wrapping up victory after 87 minutes.
Bruguera booked his place with a 6-1, 2-6, 6-3 win over defending champion and sixth seed, Petr Korda of the Czech Republic.
Wayne Ferreira guided South Africa into the final of the Hopman Cup by playing a major part in both their victories in their 2-1 victory over Romania in Perth yesterday.
The world No 10 levelled the tie with a 7-6, 7-6 victory over Adrian Voinea and then combined with Amanda Coetzer to win the doubles.
Romania, who needed to win the tie to stay in the eight-team tournament, were given a glimmer of hope when the world No 11, Irina Spirlea, beat Coetzer 5-7, 6-4, 6-1.
But there was no stopping South Africa as the third seeds maintained their unbeaten run to earn a place in the final against the United States today.
South Africa can partly credit their their progress to the final to Switzerland's Marc Rosset, who retired with a back problem when leading Ferreira 6- 0, 2-1 on Wednesday.
The second-seeded Swiss were then forced to default the doubles to give South Africa an unlikely 2-1 victory. Rosset showed no signs of his injury yesterday when he beat Germany's Bernd Karbacher in straight sets in the other Group B tie.
Martina Hingis, the world No 6, had her third consecutive straight-sets victory in the event when she beat Petra Begerow 6-1, 6-1 in just 47 minutes. The Swiss pair combined to win the doubles to take the tie 3-0.Reuse content