"I think he played a great match over nearly four hours," del Potro said. "But in every (important) moment ... he played an unbelievable shot. In break-point down, he served well. He made winners with forehands, backhands, and he played always down the line very often."
Bautista Agut had only ever played two five-set matches, losing both, and is now into the third round of a Grand Slam tournament for the first time.
Del Potro won his 18th career singles title last week by beating Bernard Tomic in the final of the Sydney International, a key warm-up event for the Australian Open, and was considered the leading contender from outside the "Big Four" for the Australian title.
"The season has just started," del Potro, the 2009 U.S. Open champion, said. "I will try to be positive for the rest of the year."
How Americans fared
At Melbourne Park
After Second Round
John Isner (13) lost first round.
Ryan Harrison lost first round.
Steve Johnson lost first round.
Bradley Klahn lost first round.
Denis Kudla lost first round.
Wayne Odesnik lost first round.
Sam Querrey to third round, vs. Fabio Fognini (15).
Michael Russell lost first round.
Tim Smyczek lost first round.
Jack Sock lost second round.
Rhyne Williams lost first round.
Donald Young to third round, vs. Kei Nishikori (16).
Serena Williams (1) to third round, vs. Daniela Hantuchova (31).
Sloane Stephens (13) to third round, vs. Elina Svitolina.
Lauren Davis to third round, vs. Eugenie Bouchard (30).
Irina Falconi lost second round.
Madison Keys lost second round.
Vania King lost first round.
Varvara Lepchenko lost second round.
Bethanie Mattek-Sands lost first round.
Christina McHale lost second round.
Alison Riske to third round, vs. Angelique Kerber (9).
Sachia Vickery lost first round.
Venus Williams lost first round.