The Swans had to settle for a point after Preston came from behind to claim a 1-1 draw at Deepdale.
Graham Potter's side, chasing a third consecutive win in all competitions, had led in the 55th minute courtesy of Courtney Baker-Richardson's third goal of the season.
The hosts, though, would earn a share of the spoils courtesy of a controversial penalty which Daniel Johnson slotted home after Connor Roberts was adjudged to have handled Jayden Stock's cross.
Preston would finish the game with ten men after sub Josh Earl was dismissed with nine minutes left.
This result moves the Swans onto 37 points from 27 games.
The Swans were unchanged for the first time under Potter, which meant Baker-Richardson kept his place up front as Oli McBurnie missed out after coming down with illness overnight.
Wilfried Bony, Jefferson Montero and Cameron Carter-Vickers were named on the bench after missing the FA Cup game at Aston Villa through sickness.
The first half was short of drama and chances in what proved a tight encounter.
The Swans carved opened the first threat after three minutes as Nathan Dyer and Kyle Naughton linked to tee up Baker-Richardson, but his shot was blocked.
Leroy Fer then dragged his shot wide when he was sent racing into the box by Naughton while Preston's opening effort came with ten minutes left of the half as Brad Potts' effort was collected at the second attempt by Mulder.
The final effort of the half saw Celina's strike take a deflection before keeper Declan Rudd tipped it wide.
Like they did in the first half, the Swans made a quick start after the restart.
Fer and Dyer did well to set up Celina, but his shot was blocked by the Preston defence.
Then, with ten minutes of the half played, the Swans got themselves in front.
Some fine work by Routledge, who controlled the ball at pace, led to him sending Celina down the left inside the box and his perfect low cross found Baker-Richardson, who tapped home from close range.
But five minutes later the celebrations turned to disbelief.
Stockley's cross struck Roberts, and referee Keith Stroud pointed to the spot for handball after being given the nod by his assistant.
Up stepped Johnson, and he sent Mulder the wrong way.
It set up a tense finish, and Mulder came to the rescue with two fine saves seconds apart to firstly deny sub Sean Maguire and then Alan Browne.
The Swans were then given a numerical advantage as sub Josh Earl - introduced at the break - was dismissed for a second booking for a foul on Mike van der Hoorn.
Substitutes Jefferson Montero and Wilfried Bony linked up in the latter stages as the Swans went in search of a winner, only for the Ivorian to nod wide.
That was the end of the action, though, as the Swans were made to settle for a point.
Preston North End: Declan Rudd, Tom Clarke (captain, Darnell Fisher, 67), Paul Huntington (Josh Earl, ht), Jordan Storey, Andy Hughes, Ben Pearson, Daniel Johnson (Sean Maguire, 75, Alan Browne, Tom Barkhuizen, Jayden Stockley, Brad Potts.
Subs: Connor Ripley, Ryan Ledson, Paul Gallagher, Lukas Nmecha.
Swansea City: Erwin Mulder, Kyle Naughton (Barrie McKay, 87), Mike van der Hoorn, Joe Rodon, Connor Roberts, Leroy Fer (captain), Matt Grimes, Nathan Dyer (Jefferson Montero, 83), Bersant Celina, Wayne Routledge, Courtney Baker-Richardson (Wilfried Bony, 75).
Subs: Kristoffer Nordfeldt, Cameron Carter-Vickers, Daniel James, Jay Fulton.