The eighth-seeded Clijsters came from a set down to defeat No. 17 Henin 2-6, 6-2, 6-3.
Clijsters made the decisive break in eighth game of the final set after Henin overhit a forehand, then closed out the match on serve.
Clijsters made 23 unforced errors to Henin's 10, but grew in confidence as the match wore on.
The win gives Clijsters a 13-12 advantage in their head-to-head record. Both players returned to Wimbledon this year after brief retirements.
The 27-year-old Clijsters will play Russian Vera Zvonareva in the quarterfinals.