Massimo Luongo fired home from Pritchard's whipped cross to open the scoring. Lee Miller nodded against a post before Carlisle did equalise through Sean O'Hanlon's header. Pritchard restored the Robins' lead with a lovely curling free-kick before substitute Dany N'Guessan tapped in Nile Rangers' cross.
The home side could have been out of sight before the break and should have opened the scoring after 29 minutes but Nicky Ajose missed from a narrow angle after rounding goalkeeper Ben Amos.
However, it was not long before Swindon were ahead. Pritchard whipped in a fine cross for Australian Luongo to fire underneath Amos in the 36th minute.
After Miller's header hit a post shortly beofre the interval, Graham Kavanagh's men came out brightly after half-time and O'Hanlon got Carlisle back on level terms when he headed a James Berrett delivery past Wes Foderingham midway through the second half.
Just three minutes later though Pritchard picked himself up after being fouled and curled a stunning free-kick past Amos to restore the Robins' lead with 72 minutes on the clock.
Sub N'Guessan, who had only been on the pitch for a few seconds, put the icing on the cake in the dying moments when he tapped in Ranger's pass for his eighth goal of the campaign.