The 6-2, 6-7, 7-6 victory means Clijsters will play for a 37th career title on Saturday against Venus Williams, who earlier cruised to a 6-3, 6-4 win over France's Marion Bartoli.
Clijsters dominated the opening set of her encounter with Henin but then, having been 3-0 up in the second, lost out in a tiebreak to allow the game into a decisive third set.
Neither of the two former world number ones, who have both made comebacks to the game, dominated on serve and Clijsters produced a double fault when serving for the match.
After losing the first two points of the tiebreak, Clijsters roared back to take a 6-3 lead but once again Henin refused to roll over.
She won the next three points to close to 6-6 before Clijsters produced two great shots -- a volley close to the net and then a forehand across the court -- to win the match.
Berdych through
Czech Tomas Berdych fought back from a set down to beat Spain's Fernando Verdasco 4-6, 7-6, 6-4 to set up his semifinal against Robin Soderling.
Berdych, the number 16 who eliminated top seed Roger Federer in the previous round, struggled in the opening set but came out on top in the tiebreak in the second and produced an aggressive display in the deciding third set.
After another impressive win, Berdych will be confident of getting through to Sunday's final. Andy Roddick and Rafa Nadal will meet in Friday's first semifinal. Soderling scored a 6-1, 6-4 win over Russian Mikhail Youzhny.
Paes-Dlouhy in final
India’s Leander Paes and Luks Dlouhy of the Czech Republic breezed past Spaniards Nicolas Almagro and Tommy Robredo 6-3, 6-0 to reach the doubles final. Paes could meet his old partner and compatriot Mahesh Bhupathi in the finals.
Fourth seeds Bhupathi and Max Mirnyi of Belarus entered the semifinals as they overcame a tough fight from Frenchmen Arnaud Clement and Jo-Wilfried Tsonga 6-4, 6-7(5), 10-4 in an hour and 38 minutes.
They will play Mariusz Fyrstenberg and Marcin Matkowski for a place in the final.