The Marlies (30-17-4) improved to 4-2-0 on their current 10-game homestand, which continues Sunday against the Oklahoma City Barons, and swept the four-game season series with the Rampage (23-22-8).
The loss snapped the Rampage's six-game winning streak and franchise-best 12-game point streak. Entering Saturday, San Antonio had earned points in 16 of its past 17 games with the club's last loss coming in a shootout against Toronto on Feb. 5.
Bobby Butler pulled San Antonio to within one with 4:56 remaining in the third, but that's as close as the Rampage would get.
Biggs scored 10 seconds in to the first period, jamming home a loose puck off a scrum in front of Rampage starter Michael Houser for his sixth of the season.
D'Amigo gave the Marlies a 2-0 lead at 10:24 of the opening period, beating Houser glove side for his 14th of the campaign. D'Amigo, who was checked on the play and went into the boards heavily, came up favouring his left hand and went directly to the Marlies dressing room, but later returned.
San Antonio defenceman Alex Petrovic was assessed a five-minute major and a game misconduct for slashing on the play.
Houser, who allowed two goals on nine shots, was replaced by Jacob Markstrom. He finished with 23 saves.