Lucas Boye and Jordan Obita scored the goals in the 2-0 win.
Championship side Reading beat League One outfit Blackpool 2-0 in a replay to reach the FA Cup fourth round.
Goals from Lucas Boye and Jordan Obita either side of half-time at Bloomfield Road ensured Reading will entertain the victors of the encounter between Carlisle and Cardiff.
Just before the break Callum Guy drilled a low effort inches wide as Blackpool nearly took the lead.
Reading took advantage when Jay Spearing failed to clear Garath McCleary's cross and Boye stabbed home three minutes from half-time.
Blackpool almost had an immediate response when Armand Gnanduillet's header from Liam Feeney's corner glanced wide.
Michael Olise nearly added Reading's second after the restart but clipped the post, before Royals stopper Sam Walker saved Matty Virtue's close-range header.
Walker later clawed away Nathan Delfouneso's header, before Boye rattled the crossbar and Omar Richards struck the post shortly after.
Blackpool goalkeeper Mark Howard kept out Obita's 82nd-minute header but the Reading man slotted home the rebound to ensure his side progressed to the next round.