As expected, the Swans lined up with Butler and Alan Tate in for the injured Paul Anderson and Dennis Lawrence as Roberto Martinez's men looked to stretch further away at the top.
They failed to make any headway against some stout defending and it was 15 minutes before Hatters keeper Dean Brill was forced to save a long-range effort from Ferrie Bodde.
Three minutes later, Darren Pratley evaded a challenge from Chris Perry to cross into the danger area, but Jason Scotland was slow to get his shot away and the visitors cleared.
Bodde produced the best pass of the evening on the half-hour when he swung a ball out wide to Andy Robinson, but the wingman's centre was easily cut out by Brill.
A snapshot from Robinson flew straight at Brill just as a disappointing first half drew to a close.
The Swans started the second period with more urgency but all too often attacks floundered when they neared the opposition goal.
They could even have found themselves a goal down on the hour when Steve Robinson drove in but Dorus de Vries leapt to his left to push behind for a corner.
Luton suffered a blow in the 69th minute when Sol Davis received a second yellow card after scything down Butler with a reckless challenge out near the touchline.
Swansea began to make full use of their numerical advantage and it was one-way traffic as they battled away against a nine-man Luton defence.
But the breakthrough finally came 11 minutes from time when Butler found space to fire in a shot that went in off the far post.
There was no way back for the battling Hatters, but the Swans were unable to add to their score.