Leonardo Jardim's men will attempt to finish off the job when Arsene Wenger returns to the principality with his Arsenal side trailing 3-1 from the first leg of the round of 16 clash and Monaco should head into that crunch clash full of confidence after a comfortable win.
Teenage striker Martial put Monaco in front 22 minutes when he was on hand to fire home at the back post and any chance of a Bastia fightback looked slim when Drissa Diakite was sent off for a professional foul on Matheus Carvalho 10 minutes later.
Layvin Kurzawa was unable to convert the resulting penalty as Alphonse Areola denied him from 12 yards, but Matheus doubled Monaco's lead two minutes before half-time with his first Ligue 1 goal after Nabil Dirar squared the ball for him.
The Brazilian then set up Martial for a third six minutes after the break and things went from bad to worse for Bastia when Giovanni Sio was also given his marching orders for a poor challenge on Kurzawa just four minutes after coming on.
Victory for Monaco ensured they are now three points behind third-placed Marseille, who host leaders Lyon on Sunday.
Christophe Mandanne's double ensured Guingamp ended a run of three-consecutive Ligue 1 defeats as Nice's poor form continued with a 2-1 home defeat.
Guingamp had failed to find the net in their losing run, but got back on track courtesy of a goal in each half from Mandanne.
Eric Bautheac had equalised for the home side 12 minutes into the second half, but Mandanne soon put Guingamp back in front and Nice were unable to respond as they slumped to a fourth defeat in a row, leaving them just five points better off than third-bottom Toulouse.
