Banton, who joined on a one-month loan deal from Crystal Palace in the January transfer window, opened the scoring after just five minutes of Saturday's League Two clash at the Recreation Ground with a low 25-yard drive that took a slight deflection and wrong-footed Jamie Young.
Aldershot hit back in the 11th minute when an unmarked Peter Vincenti tapped in from eight yards after Jake Cole had saved Danny Hylton's effort.
In a rare moment of quality, Vincenti controlled a long cross-field pass beautifully but his quick shot from the edge of the box was saved by Cole with half an hour gone.
And just as Aldershot looked to be taking control, they were caught on the counter-attack. Reuben Reid crossed for Banton, who coolly cut inside and curled the ball past Young for his second goal with 40 minutes gone.
Aldershot did their best to up the ante after the break and almost levelled on the hour when Danny Rose struck a post with a sweetly struck volley from just outside the area.
The hosts continued to press and Hylton somehow managed to slice a volley over the bar from six yards out in the 81st minute as Argyle held out to leapfrog the Shots, who drop into League Two's relegation zone.