An enthralling advert for second-tier football at the Liberty Stadium leaves the table tantalisingly close with six matches remaining, with just one point - and the merest of goal difference - separating second-placed Norwich, third-placed Cardiff and Swans in fourth.
The hosts overcame a nervy start to break the deadlock after five minutes courtesy of a superb free-kick from on-loan Chelsea striker Fabio Borini, his third goal in three games.
Mark Gower showed great technique to drill home a stunning second from fully 20 yards just before the half-hour mark, picking the perfect moment to grab his first of the season.
The Canaries made almost all of the running after the break and enjoyed their fair share of chances to get back into it, but Swansea held firm and added an injury-time third through on-loan Ipswich man Tamas Priskin to inflict only a second defeat in 19 matches on Paul Lambert's side.
The result will also have left a smile on the face of QPR boss Neil Warnock, who has seen his table-toppers keep their nine-point lead intact despite a stunning 4-1 defeat at bottom club Scunthorpe.
Swansea certainly had the early jitters and were indebted to Dorus de Vries for two great stops to deny Daniel Pacheco and Grant Holt, the latter of whom appeared certain to score.
And amid a frenetic end-to-end opening, Borini broke the deadlock with a great 25-yard free-kick into the top corner which left John Ruddy helpless.
Having made such a bright start, the Canaries struggled to get a grip on proceedings immediately following Swansea's opener but slowly worked their way back into the encounter.
Yet they were soon presented with a tough task as Swansea doubled their advantage in the 29th minute.
Angel Rangel's shot was parried by Ruddy and only cleared by Zak Whitbread as far as Gower, who showed great skill to drill the ball into the net from distance.
Swansea could smell blood and went in search of a third before half-time.
A series of corners and half-chances failed to come to anything although Ruddy had to be alert to deny Borini from 12 yards.
The opening 45 minutes would have left Swans boss Brendan Rodgers by far the happier of the two managers, and Lambert went some way to changing that at the break.
With Simeon Jackson replacing Andrew Surman, Norwich flew out of the blocks at the start of the second half and the unmarked Holt sent a header disappointingly wide from six yards.
Andrew Crofts looks to grabbed the crucial lifeline the visitors craved in the 57th minute but his well-taken volley flew narrowly wide.
Swansea have conceded just nine league goals at home all season and it was easy to see why in the 72nd minute as De Vries produced a great double save to twice keep out substitute Korey Smith.
Rangel saw a shot deflected narrowly wide at the other end as Swansea looked to move out of sight.
And Priskin did add a third late on, winning a 50/50 with Ruddy to send the ball into an empty net, leaving all eyes on Tuesday's eagerly-anticipated next round of fixtures.