Clijsters, who made her return to tennis at this event one year after a two-year break from the sport, was staring defeat in the face after losing her first set of the tournament and trailing 3-5 in the second.
But the Russian passed up three championship points, and Clijsters rallied - after a 74-minute rain delay to nick the second set on the tie-break en route to a 2-6 7-6 6-2 victory.
Now ranked world number three, Clijsters admitted that the turnaround was unexpected. "I'm a little confused. I was so close to losing, then this dark cloud came, and it changed,” she said. "I guess I forgot my serve back in the hotel, so I went back quickly to get it.”
The victory gave Clijsters her 38th career singles title, having already taken crowns in 2010 at Brisbane and Miami.
Earlier, Flemish player Yanina Wickmayer was beaten in the quarter-finals by Russian teenager Anastasia Pavlyuchenkova 7-5 3-6 6-1. Leading 5-1 in the opening set on a heat-baked court, the 12th seeded Wickmayer soon began suffering in the oppressive humidity, allowing Pavlyuchenkova to rally back.