Swansea were spared an embarrassing evening against npower League One side Crawley Town after Garry Monk produced a late winner in a 3-2 victory at Broadfield Stadium.
With the score level at 2-2 and extra-time beckoning, Monk nodded home a corner by Wayne Routledge in the 90th minute as Swansea evaded a third successive defeat.
The Barclays Premier League club looked on course for an easy night as their early dominance was rewarded when Miguel Michu pounced. But Josh Simpson and Hope Akpan struck to give Crawley, who lost to Manchester United in the fifth round of the FA Cup two seasons ago, hope of humbling their top-flight opponents.
Had the finishing skills of Jonathan Forte matched his surging runs from midfield, a prized scalp would have been assured. However, substitute Danny Graham equalised in the 76th minute, sparking a lively spell from Swansea who finally regained the lead through Monk.
Meanwhile, Swindon are through to the last 16 after an impressive 3-1 victory over Burnley at the County Ground.
The Clarets, of the npower Championship, made the brighter start, with former Robins striker Charlie Austin going to close to opening the scoring when he saw an early header cleared off the line by left-back Jay McEveley.
But after 19 minutes, McEveley turned provider as the home side took the lead against the run of play. His whipped, left-wing cross WAS neatly turned in on the half-volley by striker Paul Benson.
Burnley continued to dominate possession - with midfielder Chris McCann and Austin both spurning decent opportunities - but it was Swindon who doubled their advantage four minutes before half-time.
After a succession of misplaced passes, the ball found its way to Andy Williams who showed a burst of pace to run clear of the Burnley defence and finish coolly past Brian Jensen.
Austin eventually marked his return to the County Ground with a scrappy tap-in after 75 minutes, but a Troy Archibald-Henville header seven minutes from time - his first for the League One side - ensured that Burnley's scalp was added to that of Stoke and Brighton in this season's competition.