Lopez looked on course for a fairly routine victory after taking the first set 6-3, but the big-serving Isner hit back by claiming the second in a tie break.
The Spaniard responded by claiming the third set 6-4, but his American opponent hit back once again, before Lopez saw out the last set 6-1.
Czech 7th seed Tomas Berdych had an easier progress to the next round, beating South African Kevin Anderson 7-6 7-6 6-1.
Both Roger Federer and Rafael Nadal enjoyed routine straight-sets victories over Lukas Lacko and Ivo Karlovic respectively, while 10th seed Nicolas Almagro ended Stanislas Wawrinka's hopes with a 7-6 6-2 6-4 win.
Philipp Kohlschreiber also enjoyed a 6-3 6-2 7-6 victory over Alejandro Falla, while Juan Martin del Potro barely broke a sweat as he defeated Lu Yen-Hsu 6-2 6-3 6-0.
And in a brilliant way to end the men's action for the day, 19-year-old Australian Bernard Tomic prevailed after an epic battle to record a 4-6 7-6 7-6 2-6 6-3 victory over 13th seed Alexandr Dolgopolov.
Results from Day 5 of the Australian Open
Feliciano Lopez def. John Isner 6-3 6-7 6-4 6-7 6-1
Tomas Berdych def. Kevin Anderson 7-6 7-6 6-1
Juan Martin del Potro def. Lu Yen-Hsu 6-2 6-3 6-0
Philipp Kohlschreiber def. Alejandro Falla 6-3 6-2 7-6
Nicolas Almagro def. Stanislas Wawrinka 7-6 6-2 6-4
Bernard Tomic def. Alexandr Dolgopolov 4-6 7-6 7-6 2-6 6-3