Nadal suffered one of the worst Grand Slam results of his career as he was stunned by fellow Spanish left-hander Fernando Verdasco in a five-set thriller which recalled their epic 2009 semi-final.
Halep, the women's world number two, soon followed him out in an almighty upset by Chinese qualifier Zhang Shuai -- who wept freely as she won her first Grand Slam match in 15 attempts.
Nadal, 29, has only ever lost once before in a Grand Slam first round, at Wimbledon 2013, but he has not gone further than the quarter-finals at the majors since he won the 2014 French Open.
"It's tough, but at the same time, I know I did everything that I can to be ready for it," said Nadal, after 45th-ranked Verdasco's 7-6 (8/6), 4-6, 3-6, 7-6 (7/4), 6-2 win in four hours, 41 minutes.
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The big upsets at least provided relief from match-fixing revelations which hit the start of the tournament after a report said top players had been under suspicion but never punished.
In the latest developments, two more players said they had been targeted by match-fixers and Australian media reported that police were keeping a close eye on the tournament's first round.
Andy Murray, a four-time finalist who is seeking his first title in Melbourne, dispatched Germany's Alexander Zverev 6-1, 6-2, 6-3 in hot conditions to move into the second round.
Temperatures of 33 Celsius (91.4 Fahrenheit) took their toll and Diego Schwartzman was stretchered off after retiring in the fourth set against John Millman with cramps.
While Murray and Muguruza motored through, seven-time Grand Slam champion Venus Williams suffered an early exit when she lost to British number one Johanna Konta 6-4, 6-2.
Williams, 35, was the oldest player in the women's draw but Konta said it would be "silly" to focus on the American's age.
Former world number one Lleyton Hewitt extended his farewell tournament into at least another match when he beat fellow Australian James Duckworth, setting up a clash with eighth seed David Ferrer.
Milos Raonic, who is now working with Carlos Moya and beat Roger Federer in this month's Brisbane final, breezed past Lucas Pouille and into the second round.
Two-time champion Victoria Azarenka enjoyed one of the most one-sided wins of her career when she "double-bagelled" Alisan Van Uytvanck 6-0, 6-0 in just 53 minutes.
France's Jeremy Chardy had an even bigger struggle, winning the fifth-set 13-11 to finally overcome Ernests Gulbis after four hours and 43 minutes.