The second-seeded Nadal was leading 6-2, 6-2 when France's Nicolas Mahut retired with an abdominal muscle injury in the first game of the third set at Arthur Ashe Stadium. The Spaniard committed only five unforced errors and saved all four break points he faced.
The fourth-seeded Murray fought back to dump Haase 6-7 (5-7), 2-6, 6-2, 6-0, 6-4. It marked the sixth time the Scot had won a match after dropping the first two sets.
Murray will battle 25th-seeded Spaniard Feliciano Lopez in the third round. Lopez advanced with a 5-7, 6-4, 7-6 (7-3), 7-6 (7-5) win over Canadian Vasek Pospisil.
Andy Roddick, who is playing on his lowest seeding ever at a Grand Slam as the 21st seed, moved on by defeating fellow American Jack Sock, 6-3, 6-3, 6-4. Roddick lost in the second round of the Open last year.
Del Potro, the 2009 U.S. Open champ, is slowly returning to form after a wrist injury cost him most of the 2010 campaign. He is seeded 18th this year and followed up an easy opening-round win over Italy's Filippo Volandri with a 6-2, 6-1, 7-5 triumph over fellow Argentine Diego Junqueira.
A pair of seeded players lost in five sets on Friday. No. 14 Stanislas Wawrinka of Switzerland fell to American Donald Young 7-6 (9-7), 3-6, 2-6, 6-3, 7-6 (7-1) and Russian Igor Kunitsyn defeated 17th-seeded Austrian Jurgen Melzer 3-6, 6-3, 1-6, 6-2, 7-6 (7-5).
Other second-round winners Friday included 24th-seeded Argentine Juan Ignacio Chela, 28th-seeded American John Isner, No. 26 Florian Mayer of Germany, France's Julien Benneteau, American Alex Bogomolov Jr. and Luxembourg's Gilles Muller.