The 25-year-old Republic of Ireland international, who joined Swansea from Hartlepool on a free transfer in the summer, pulled United apart.
The Sheffield side, knocked out at the same stage last season by Colchester and looking for a good cup run, fielded 10 players with Premiership experience.
But it was League One promotion candidates Swansea who carved out the first opening after youngster Kevan Hurst, recalled from a loan spell at Chesterfield, hit a wayward back pass. Rory Fallon steamed in to drill in a low strike which was blocked by Paul Gerrard before the ball was hacked away.
Sheffield United had plenty of possession but were closed down by the hardworking Welsh side without four key players including talisman Lee Trundle, serving a three-match ban.
They tested Gerrard again on 32 minutes after centre-back Leigh Bromby stopped Butler in his tracks with a strong challenge, the ball rolled to Fallon who fired in a left-foot shot, which was smothered on the line by the diving keeper.
Butler went close minutes later with a dipping free kick from 20 yards which took a wicked deflection off the head of Christian Nade as the ball curled the wrong side of the woodwork.
United, disjointed and struggling to string a pass together, finally tested Swansea in the 42nd minute. Nick Montgomery crossed to Alan Quinn whose close range header flashed inches over the target before Hurst was then foiled by Swansea keeper Willy Gueret, who blocked the midfielder's shot on the turn after good work from Colin Kazim-Richards.
Hurst squandered a chance after the unselfish Nade passed inside but his low drive hit the outside of the post before Butler then hit United with a two-goal salvo.
Adebayo Akinfenwa did the hard work in the 53rd minute as he cut inside and had his shot blocked by centre-back Bromby. But the ball ran towards Butler and he slotted it past Gerrard from 15 yards.
Butler added a second six minutes later when Akinfenwa had been challenged by David Sommeil, allowing the midfielder to then run on to the loose ball to slide it under Gerrard's leg.
Quinn then saw his header saved by Gueret before Swansea finished off the Blades in the 67th minute. Full-back Derek Geary's rash challenge upended Butler as Leon Britton stepped up to coolly beat Gerrard from the penalty spot.
Swansea went close again with minutes to go, as Gerrard was scrambling at the foot of his post to keep out Britton's free kick.