The 23-year-old Halep, of Romania, chasing her first grand slam singles title, came out strong against the Belarussian after an 85-minute, third-set rain delay to secure a 6-3 4-6 6-4 victory and a last-four clash against Italy's Flavia Pennetta.
"It was a tough match. I’m really happy that I could win, I don’t know where it comes, the power to win this match," said the diminutive, but hard-hitting Halep.
Halep was run ragged in the second set by Azarenka who sent her scurrying from corner to corner as she fought back to level the quarter-final at one set apiece.
A light rain forced them off the court in the fourth game of the third set but when they returned to Arthur Ashe Stadium, a revived Halep took command.
"I was a bit tired after the second set and that break helped me. Thanks God, for raining," Halep said in an on-court interview.
"I found the power to give everything to win this one because I really wanted to play first time the semi-finals here."
After an opening set dominated by Halep, two-times Australian Open winner Azarenka, who has slipped to 20th in the world rankings after battling injuries the last two seasons, battled back.
Emotions ran high with both players shrieking in frustration after mistakes and roaring in self-encouragement after an important point.
After the break, Halep served an ace on the first point back on court to level the third set at 2-2, before breaking in the seventh game for the margin she needed to reach the semi-final.
Halep was cheered on by a noisy contingent of flag-waving Romanians and a special guest in the player's box, five-times Olympic gold-medal winning gymnast Comaneci.
"It was great to have a great champion in my box. It was a good day for all of us," Halep said.
Pennetta, 33, ousted twice Wimbledon winner Petra Kvitova, the fifth-seeded Czech, in three sets to advance.
Top seed Serena Williams, bidding to complete the fourth women's calendar-year Grand Slam sweep, faces Roberta Vinci of Italy in Thursday's other scheduled semi-final.
(Editing by Frank Pingue)
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