Fourth-seed Goran Ivanisevic had a much easier tie, advancing to the next round after brushing aside Christophe Van Garsse, of Belgium, 6-3, 6-0 in 43 minutes.
British No 1 Henman ought to have wrapped up a straight sets win but squandered three match points in the second set to let Tarango off the hook.
Henman went on to beat Tarango in the third set and secure a semi-final spot with a 6-4, 6-7, 6-4 victory that took two hours and 34 minutes.
However, Henman, the world No7, knows he cannot afford to repeat the lack of concentration which enabled Tarango to take the second set tie- break if he is to go on and win the tournament.
"Jeff put up a strong resistance," admitted Henman, who fired 21 aces during the match.
Despite his defeat Tarango, ranked 74th in the world, still managed a smile. He said: "I did everything that I could. I think my form has really come on."
After an assured start by Henman in the first set, a real dogfight ensued in the next, with a furious exchange before Tarango squared the match in the marathon tie-break. Henman responded well to the loss of the second set, breaking Tarango in the opening game of the third and opening a 3- 0 lead. Tarango clawed his way back to 4-3 down but Henman held his nerve to kill off the American's comeback.
He fell back on intelligent and elegant play and asserted himself in the third to earn a semi-final meeting with Karim Alami, who beat his fellow Moroccan Hicham Arazi 6-1 6-7 6-4.
Henman was flying the flag for Britain following the surprise exit of second seed Greg Rusedski, who crashed out against Germany's Bernd Karbacher in the opening round.
Henman had no trouble in disposing of the Dutchman Sjeng Schalken in his first-round match. However, the erratic form in evidence against Tarango had surfaced in his second round victory over Morocco's Younes El Anaoui, where he struggled early on and lost the opening set before getting his act together. Henman has set his heart on winning the title, making up for last year's quarter-final exit against Petr Korda.
Meanwhile, Sweden were set to play Australia in today's Hopman Cup final after Jonas Bjorkman and Asa Carlsson came from behind to defeat Switzerland's Ivo Heuberger and Martina Hingis 2-1 .
Hingis won the opening singles tie 6-2,6-2, before Bjorkman drubbed her partner Heuberger 6-2, 6-0 to level the tie. The Swedes claimed the mixed doubles 2-6 ,6-3, 6-4.
The relief was evident on the face of Bjorkman, who has been required to win all of his singles games during the mixed teams championship because Carlsson has lost all three of hers.
The final will pit the Swedes against the big-serving Mark Philippoussis, last year's losing US Open finalist, and the 15-year-old prodigy Jelena Dokic.
Bjorkman was delighted at needing less than an hour to dispose of Heuberger, who made an unacceptable 34 unforced errors. "I never let him into the match, but Ivo didn't have one of his best matches," Bjorkman said. "I'm very happy and pleased that I've won all three singles matches."
The seven-time Wimbledon champion Steffi Graf overpowered the American teenager Serena Williams 6-2, 7-6 to reach the final of the Super-Power Challenge Cup in Hong Kong.
Graf faces Williams' sister Venus, who beat Anna Kournikova of Russia 6-4, 6-3 in the other semi-final.Reuse content