Howe is set to become Clarets boss after confirming he is leaving his position at Bournemouth, revealing after Friday night's 2-1 League One defeat at Colchester that the match was his last in charge of the Cherries.
He is poised to be confirmed as as successor to Brian Laws after Stuart Gray presided over his final game as caretaker boss.
Chances were few and far between against Neil Warnock's side as defences remained firmly on top throughout.
Gray named an unchanged side, keeping faith with the team that knocked Port Vale out of the FA Cup last weekend.
The visitors included former Burnley loanee Bradley Orr in their side, along with recalled leading scorer Adel Taarabt.
Rangers showed all the confidence befitting of league leaders as they dominated the opening exchanges and put Burnley on the back foot as Howe watched on.
Warnock's side fashioned the first goalscoring opportunity in the eighth minute when midfielder Shaun Derry fired goalwards from 25 yards.
The ball look destined to find the net but Clarets goalkeeper Lee Grant produced a fine save to tip the ball round a post.
Two minutes later, Taarabt tried his luck with an ambitious low drive from a tight angle, but the effort did not trouble Grant.
Moments later Burnley had their first chance to threaten but Tyrone Mears' free-kick flew harmlessly over the crossbar from 20 yards.
In the 16th minute, the pendulum swing back in Rangers' favour and Taarabt's 12-yard shot was well saved by Grant.
Rangers were in total control and Burnley struggled to get past second gear in the first half.
They threatened through Clarke Carlisle and Jay Rodriguez, although the Clarets knew an improvement was needed after the restart.
Yet Rangers threatened again three minutes in the second half when Taarabt hit a 30-yard free-kick just wide of the target.
In the 68th minute, Rangers striker Rob Hulse hit a right-foot shot over the crossbar from six yards.
Moments later Burnley caretaker boss Gray replaced Chris Iwelumo with Steven Thompson in a bid to breath new life into his faltering attack.
However, genuine goalscoring opportunities remained scarce as conditions made freeflowing football difficult.
With 19 minutes remaining, Tommy Smith engineered the space to hit a 12-yard strike which drew a fine block by Carlisle.
Petter Vaagan Moen went close for Rangers late on but Carlisle produced another fine block to avert the danger.