Howe 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.
Clarets keeper Lee Grant saved from Shaun Derry and Adel Taarabt in the first half, and after the break Rob Hulse fired over.
With 19 minutes remaining, Tommy Smith engineered the space to hit a 12-yard strike which drew a fine block by ex-Hoops defender Clarke Carlisle.
Petter Vaagan Moen went close for Rangers late on but Carlisle produced another block to avert the danger.
Source: PA
Source: PA