The French Open finalist was on course to continue her impressive record at this year's majors but came unstuck against the Croatian who is ranked 119 places beneath her in the world.
Having broken three times early on, the world number two led 5-2 before allowing her opponent back into the set.
Lucic-Baroni won the next four games to help force the opening set to a tie-break, in which Halep was beaten without ever having managed to forge ahead.
After a first set in which Halep won only 58 per cent of her first service points, the Romanian quickly found herself 3-1 down in the second.
Halep was again broken in the seventh before Lucic-Baroni kept her cool to win the final three games and wrap up progression.
It is the first time since Wimbledon in 1999 that Lucic-Baroni has made the fourth round at a grand slam and her reward is a meeting with 13th seed Sara Errani.
The Italian accounted for two-time US Open winner Venus Williams 6-0 0-6 7-6 (7-5).