Tommy Haas also finished up the third set of one victory and then went out and earned another to grab his quarterfinal berth, but second-seeded Kei Nishikori came up short in his bid for two wins in the same day.
Thursday's busy schedule was brought about by rains that wiped out many of Wednesday's matches.
The goal for Thursday was to complete the second round and establish the quarterfinal pairings. That goal was achieved, but it created a heavy workload for some players.
Del Potro, seeded first in the event, opened the day with a 6-1, 7-5 decision over Ryan Harrison and he then defeated Bernard Tomic 6-3, 6-3.
Anderson eliminated James Duckworth early in the day 6-3, 3-6, 6-4 and then dispatched Mardy Fish 7-6 (7-2), 6-1.
Haas had split the first two sets of his match with Tim Smyczek on Wednesday before the rains came and then finished off the victory Thursday by capturing the third set 6-4. Haas next won over Ivan Dodig 6-4, 4-6, 7-5.
Haas will meet Grigor Dimitrov after Dimitrov won his only match of the day against Sam Querrey 4-6, 6-3, 7-6 (11-9).
John Isner, seeking his second tournament title in as many weeks, reached the quarterfinals with a 7-5, 7-5 decision over Somdev Devvarman. Marcos Baghdatis eliminated Nishikori 6-1, 6-2 to set up a meeting with Isner.
Nishikori lost to Baghdatis after winning over Jack Sock earlier in the day 7-5, 6-2.
The other quarterfinal duel will send Dmitry Tursunov against Marinko Matosevic. They each played just one match Thursday -- Tursunov getting past Radek Stepanek 6-2, 6-1 and Matosevic downing Milos Raonic 7-5, 7-6 (9-7).