Clijsters looked vulnerable throughout the second set and had to save a matchpoint at 4-5.
Meanwhile, Clijsters, the 2005 Miami champion, needed four match points to beat Henin 6-2 6-7 7-6.
Golovin admitted she was frustrated at not finishing off Clijsters when she had her chance.
Steffi Graf did it in 1994 and 1996, and Kim Clijsters won both in 2005.
She has lost Key Biscayne finals to Kim Clijsters, Svetlana Kuznetsova, Victoria Azarenka and Agnieszka Radwanska.
"Today I did not play well, " said Clijsters, who had been out since last October.
Belgians Kim Clijsters and Justine Henin, seeded one and two for the tournament, both received first-round byes.
"Before I think you all thought I'm a mental case, " she told the crowd after defeating Clijsters.
Dokic raced on to victory in 64 minutes to book a date with third seed Kim Clijsters.
Clijsters' breakthrough in the second set came after breaking Wozniacki to lead 4-2 and take the next game.
Clijsters was impressed by her compatriot's comeback match and believes she will will quickly return to the top.
Clijsters will next face Russian 23rd seed Alisa Kleybanova, who beat Bulgaria's Tsvetana Pironkova 6-7 (5-7) 6-3 6-1.
Last year, Clijsters became the first mother to take home a major trophy since Evonne Cawley in 1980.
Clijsters will next face unseeded American Christina McHale, who had a 6-2 6-4 win over Japan's Ayumi Morita.
"We're colleagues and friends, a combination, and it doesn't matter if we're playing against each other, " said Clijsters.
Hantuchova's resolve seemed to fizzle out after that and two breaks in the second set secured Clijsters' victory.
Clijsters, seemingly charmed, was in the midst of another astonishing comeback against Victoria Azarenka in the semifinals, then crumbled.
Henin and Clijsters are tied at 12 wins apiece from their 24 meetings.
Safina defeated Slovenia's Katarina Srebotnik 6-2 6-4 to ensure her showdown with Clijsters.
"I felt good out there today, " Clijsters told the WTA Tour Web site.
Clijsters will next play Karolina Sprem of Croatia after the world number 104 beat qualifier Bethanie Mattek-Sands 6-3 6-4.
In the day's final tie Belgium , without Justine Henin-Hardenne and Kim Clijsters, took the lead against Spain .
The unseeded Clijsters is playing in her second tournament this season after four months out with a wrist injury.
The resulting penalty point for a code violation handed the match to Clijsters.
"I wanted to play again so badly and I am really surprised everything went so well, " Clijsters said afterwards.
"If she was injury-free she's the toughest to beat out there, " said Clijsters.
And Clijsters again dismissed suggestions that she and Henin-Hardenne do not get on.
But Bartoli evened it up at 4-4 before a further break of service saw Clijsters one set to the good.
Clijsters immediately lit up the featured night match by winning the first four games with strong play from the baseline.
Henin's fellow-returning Belgian Kim Clijsters hardly needed to raise a sweat as she beat Canadian qualifier Valerie Tetreault 6-0 6-4.
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