World Cup - Messi inspires Argentina to big win
Angel Di Maria added the fourth 15 minutes from time.
Argentina took 20 minutes to break Ecuador down before Aguero opened the floodgates.
Messi lay on the second for Higuain after a superb run in which he shook off three defenders and then scored his 23rd for Argentina following another run from halfway and a one-two with Higuain in a high-tempo 11 minutes that left Ecuador reeling.
"We're always looking for the connection with our fans and today was impressive. We have to carry on like this, united to the end," Messi said after the crowd chanted his name.
Argentina have a bye in next weekend's round of matches and instead will play arch-rivals Brazil in a friendly in the United States.