Collins, score of four against Portsmouth in midweek, netted in between Andy Williams' double before substitute Raffaele De Vita completed another Robins rout.
Paolo Di Canio's side have now scored 14 goal in their last three matches, having beaten Tranmere and Pompey by five each and they could have done the same to Carlisle.
Swindon were ahead in the 16th minute when Williams took a pass from Alan McCormack before beating goalkeeper Mark Gillespie.
Irish striker Collins made it 2-0 after 36 minutes with a six-yard header after being picked out by a cross from Matt Ritchie.
Williams got his second goal in the 55th minute, Ritchie was again the creator with a cross to the far post from the right.
De Vita, a replacement for Ritchie after 68 minutes, got on the scoresheet with 10 minutes remaining after Gillespie had parried a shot from Gary Roberts.
As Carlisle crumbled, Tommy Miller hit the crossbar and Roberts was inches wide with a late shot.