Escoboza, who had previously scored only one goal in his career for Santos, put "Los Guerreros" ahead in the 49th, sent in a cross for Aaron Galindo to head in seven minutes later and added a finale in the 62nd. Marc Crosas tacked on a penalty in the 77th.
The win gave Santos, last year's Champions League runner-up, nine points and a six-point lead in Group 1 over Toronto FC, which has two games remaining.
The loss eliminated Aguila from contention with a third straight loss and having been outscored 14-1.
Aguila had the early initiative with Henri Romero shooting high and Isido Guttierez testing Santos keeper Miguel Bacerra within the first nine minutes.
But Santos was able to get more possession and had shots by Crosas, Candido Ramirez and Osmar Mares within two minutes of each other midway through the first half.
Santos appeared far more determined at the start of the second half and went ahead when Rodolfo Salinas played a diagonal ball into the area, where Escoboza met it at the edge of the six and volleyed it past keeper Benji Villalobos.
Escoboza, who has played only two games in the Mexican league this year and whose only other goal came a year ago against the Colorado Rapids in the Champions League, then sent a curling ball to the six, where Galindo nodded it in.
He scored his second with a run down the left side, turning along the byline and beating Villalobos to the far side.
Crosas completed the scoring after Darwin Bonilla tripped Mario Cardenas as the 19-year-old Mexican attacker entered the top of the penalty area.
The win was a fourth straight in the Champions League for Santos since losing the first leg of last season's final to Monterrey in April.
The result left Aguila, which replaced Villalobos in the 67th with Manuel Gonzalez because of an apparent injury, with only one win in its last seven games overall.