Halep, the women's world No.2, soon followed him out in an almighty 6-4, 6-3 upset by Chinese qualifier Zhang Shuai - who wept freely as she won her first Grand Slam match in 15 attempts.
It was the second opening-round upset by a Chinese qualifier at the tournament after Wang Qiang beat former Melbourne Park semifinalist Sloane -Stephens on Monday.
Zhang will face France's Alize Cornet in the second round on Thursday, her 27th birthday.
While Halep's defeat to Zhang, the world No.133, came out of the blue, it was Nadal's loss which created concern as the 14-time Grand Slam winner increasingly looks a fading force.
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 quarterfinals 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.
Andy Murray, a four-time finalist who is seeking his first win in Melbourne, dispatched Germany's Alexander Zverev 6-1, 6-2, 6-3 in hot conditions to move into the second round.
Rising star Garbine Muguruza beat Estonian debutante Anett Kontaveit 6-0, 6-4 in one hour.
Seven-time Grand Slam champion Venus Williams, 35, suffered an early exit when she lost to British No.1 -Johanna Konta 6-4, 6-2.
Former world No.1 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.
Two-time champion Victoria Azarenka enjoyed one of the most one-sided wins of her career when she "double-bageled" Alisan van Uytvanck 6-0, 6-0 in just 53 minutes.
