The French Open finalist moves on to face Slovakian Jana Cepelova, a 2-6 7-5 6-1 winner over Spain's Maria-Teresa Torro-Flor, in the second round of the season's last grand slam.
But the 22-year-old Romanian had a tricky time getting by Collins, a U.S. college champion from the University of Virginia.
Down a break at 3-4, the 20-year-old American brought the set back on serve at 4-all and with her confidence growing the collegian ran away with the decider by taking advantage of a slew of errors from Halep.
That shock seemed to snap the Romanian back to attention, and bring her groundstrokes under control as she roared to victory over Collins, who was playing her first tour-level main draw match.
"She played a tough match, I want to congratulate her," world number two Halep said in an on-court interview. "First set I was a little bit nervous. This court is huge.
"It's my best ranking ever and best moment of my life. I have to enjoy it, but it's not easy. Everybody is telling me I have chances to win this title."
Halep, who broke through last season by notching her first six career tour titles, has two titles this season and finished runner-up to Maria Sharapova at Roland Garros in her first grand slam final.
(Editing by Frank Pingue)
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