With Guidolin still being treated for a chest infection at a London hospital, first-team coach Alan Curtis took charge once more to oversee a victory which moves them nine points clear of the Barclays Premier League zone.
Gylfi Sigurdsson settled the contest after 61 minutes with his sixth goal in 10 games, sliding home the pass of substitute Leroy Fer in a composed fashion, at odds with much of what had gone before.
Norwich's position is looking increasingly perilous after an eighth defeat in nine games, and much of their good work in an even first half was undone when Swansea applied pressure after the interval.
Gianni Infantino was among the crowd after travelling from the International Football Association Board meeting in Cardiff and the new FIFA president was served up a contest high on energy, but low on quality.
Swansea's morale had been raised by their shock midweek win at Arsenal which put six points between themselves and Norwich, but it was not translated into greater confidence on the pitch as passes were misplaced with increasing regularity.
The pattern was set by Alberto Paloschi's mis-kick and, while Nathan Redmond warmed Lukas Fabianski's at the other end from an acute angle, Norwich also found openings hard to come by.
Canaries boss Alex Neil, however, would have been delighted by his side's work ethic, even if Cameron Jerome and Robbie Brady overstepped the mark to earn yellow cards.
Brady soon limped out of the action, although his pain would have been greater had Andre Ayew not headed over from Angel Rangel's cross after the Norwich man had carelessly conceded possession.
Swansea full-back Neil Taylor became the third player booked in a frantic first period which included Wayne Routledge failing to get his shot away when the Norwich goal appeared to open up.
Norwich did manage an on-target attempt in the final minute of the half when Steven Naismith laid the ball to Jerome and Fabianski pushed his 20-yard effort to safety.
Swansea's response saw a swift attack which ended with Ayew tumbling under Timm Klose's challenge inside the area, although referee Craig Pawson correctly adjudged that the Ghanaian was looking for the foul and contact was minimal.
Paloschi was taken off at half-time, with Curtis pushing Ayew up front and Modou Barrow introduced on the right.
The move had the desired effect as Swansea started to enjoy greater possession and territory and Norwich's growing anxiety resulted in bookings for Ryan Bennett, Russell Martin and Redmond.
Barrow and Ayew both fired over the top before Swansea finally found the bit of quality they had been striving for just after the hour mark.
Jack Cork freed Fer down the right and the Dutchman's slide-rule pass allowed the unmarked Sigurdsson to pick out the bottom corner from 14 yards.
Routledge almost added another when he was thwarted at the near-post by John Ruddy and the Norwich goalkeeper excelled himself late on when he acrobatically tipped away Sigurdsson's free-kick.
Norwich almost claimed a point when Routledge's poor clearance fell to Redmond, but the winger's shot went a yard wide and Fabianski held on to substitute Patrick Bamford's near-post effort right at the death.
Source : PA
Source: PA