Cresswell guided home Eddie Lewis' free-kick to break the deadlock just before half-time and then Butler capped the win with a fine effort seven minutes from full-time.
United could have won by more but it is the collection of three valuable points that will be at the forefront of manager Kevin Blackwell's mind.
The win maintained Leeds' slim hopes of catching second-placed Sheffield United and makes United's position in the play-offs almost assured.
Rangers provided little attacking threat, with Leeds keeper Neil Sullivan troubled only once when dealing with Keith Lowe's header 10 minutes into the second half.
The patched up visitors had four players making their debut and their lack of cohesion ultimately proved costly.
Boss Ian Holloway boosted his squad less than four hours before kick-off with the signing of Sheffield United reserve keeper Phil Barnes in a desperate bid to solve his goalkeeping problem after Simon Royce and Jake Cole were both ruled out through injury.
Barnes signed for the club on a seven-day loan at 11.30am and was thrown straight into the action little more than three hours later.
Holloway also handed debuts to Marcin Kus, Leon Clarke and Lowe while Leeds manager Blackwell introduced David Healy into the starting line-up after United's midweek draw at Ipswich.
Both sides showed plenty of effort but there was little quality on show during a disappointing first half.
Lewis was Leeds' most threatening player, probing the Rangers defence down the left flank and delivering a string of crosses.
And it was Lewis who provided the opportunity for Cresswell to open the scoring just before the break with a perfectly weighted free-kick.
Cresswell was quickest to react and sent a looping header over the stranded Barnes and in off the post.
Butler's late effort was again the result of a dangerous Lewis cross, with the Leeds skipper powering home a magnificent header to seal United's 10th home win of the season.