George Baldock sent Sheffield United ahead just past the hour following a tight first period, but Oliver McBurnie levelled the scores in the 71st minute before Yan Dhanda came off the bench to win it for Graham Potter's side.
That would prove to be on the only time either keeper was tested in a cagey first half, however, with neither side able to really get going in the final third.
A contentious talking point would arrive shortly before the interval, though, after Chris Basham went to ground inside the opposition box.
Replays showed that Federico Fernandez did not make any contact with the Sheffield United defender, explaining the furious reaction from Swansea's players.
Summer signing David McGoldrick fired a deflected shot over the crossbar moments later, but despite the Blades' endeavour they simply could not create any clear openings.
It was also a quiet start to the second period, but the breakthrough came just past the hour.
Indeed, Sheffield United took the lead in the 62nd minute when Baldock found the bottom corner with a smart finish following a super cross from John Lundstram.
Henderson had to make a super save to keep out a flicked header from Jay Fulton 20 minutes from time, but Swansea were level in the 71st minute when McBurnie smashed home from close range after Henderson had made another wonderful stop to prevent an own goal.
McBurnie then almost sent Swansea ahead 12 minutes from time when he met a cross from Jefferson Montero, but the striker's header just missed the far post.
The Welsh outfit came close once again in the 83rd minute when Barrie McKay struck one from distance, and the midfielder's effort smashed off the crossbar.
Swansea finally scored a second in the 85th minute, however, when Dhanda - only on the field for a matter of seconds - found the back of the net following more good work from Montero in a wide position.
John Egan had a half-chance to level for the home side in what was the final kick of the match, but the centre-back's effort was straight into the grateful arms of Swansea stopper Kristoffer Nordfeldt.
Swansea have risen into fifth position in the Championship table on the opening weekend, with Sheffield United down in 21st as the Blades start with a defeat.
SHEFFIELD UNITED (3-5-2): Henderson; O'Connell, Egan, Basham (Duffy 87'); Stevens, Evans, Fleck, Lundstram (Sharp 79'), Baldock; McGoldrick (Woodburn 72'), Clarke
SWANSEA (4-2-3-1): Nordfeldt; Roberts, Fernandez, Van der Hoorn, Olsson (Grimes 72'); Fulton (Dhanda 85'), Carroll; Asoro (Montero 64'), Celina, McKay; McBurnie