Second-half goals from Lucas Albertengo and substitute Nicolas Royon saw the Primera Division side prevail in their last 16 fixture at the Estadio Oscar Carlos Boero on Tuesday.
Confident after ending a run of back-to-back league defeats against Gimnasia La Plata 2-0 on Saturday, Rafaela made the breakthrough eight minutes into the second half.
After Talleres goalkeeper Federico Costas failed to deal with a header from a corner, Albertengo reacted quickest to tuck away the rebound for his second goal in as many games.
Rafaela doubled their advantage in the 68th minute thanks to Royon, who had only been on the pitch for six minutes after replacing Nicolas Orsini.
Costas was at the centre of the action again, guilty of mistiming his attempt to fist the ball away to safety as Royon coolly headed home into an empty net - his second goal in less than a week.
Talleres - competing in the Torneo Federal A - were given a glimmer of hope with five minutes remaining, when substitute Marcos Godoy slotted the ball past Esteban Conde but Rafaela held on for victory.
Meanwhile, Wednesday's fixture between Huracan and top-flight side Banfield was postponed due to a lack of police.
The decision was made on Tuesday and the possibility of moving the game to La Bombonera was reportedly raised, however Boca Juniors refused to lend their facilities.
