Former World No. 1 Murray was looking to reach a Grand Slam quarterfinals for the first time in six years.
Murray beat Thanasi Kokkinakis in a stunning second round match which lasted five hours, 50 minutes, ending at 4:05 a.m. local time to set up his tie with world No. 25 Bautista Agut.
After a slow start, Murray valiantly fought back to draw 1-1 after two sets. The 35-year-old could not stage a dramatic comeback, like he did in the previous round, as Bautista Agut recovered to win the final two sets.
The result means there are no British competitors left in either Australian Open singles draw.