The 34-year-old Swede saved a match point in a fourth set tiebreak before finally claiming a 7-6 (7/3), 4-6, 6-7 (5/7), 7-6 (9/7), 6-4 victory after four hours and three minutes of play that was spread over nearly seven hours because of two rain interruptions.
Björkman’s reward for his Herculean efforts was a last four meeting with defending champion Roger Federer, who was looking unstoppable as he swept Mario Ancic off court earlier in the day.
It was a case of missed opportunities for Stepanek, who was cheered on by his girlfriend Martina Hingis, but a typically gritty display from Björkman, albeit not one which suggested he will trouble Fedrer on Friday.
Björkman had taken the first set in a tiebreak after the second rain break, having failed to serve it out when he was leading 5-3.
But Stepanek began to get on top in the second, which he claimed 6-4 with a tenth game break.
After getting in front by winning the third set tie-break, the Czech broke his 34-year-old opponent in the third game of the fourth and hammered home the advantage with a service game to love to lead 3-1.
But a heavy fall as he served for the match at 5-4 appeared to disrupt his concentration and handed Björkman a lifeline.
The Swede grabbed it, saving a match point before winning an extremely edgy tie-break 9/7 to send the match into a fifth set.
Björkman claimed a break in the first game of the final set. Stepanek cancelled that one out to make it 3-3 but was unable to hold serve in the ninth game of the set and the Swede held his nerve to close out the match.
It will be Björkman’s second Grand Slam semi-final appearance following his run to the last four of the 1997 US Open, where he lost to Greg Rusedski.