Goals from Robert Huth and Marc Wilson got the Potters back to winning ways while Jones came close to ending his scoring drought when he was denied by a magnificent Paul Robinson save.
Pulis said: 'Kenwyne played very well and led the line. I have no doubt that Kenwyne is going to be fine. He just needs a bit of luck and one to go in off someone else's backside.
Battle: Kenwyne Jones (right) keeps the ball from Blackburn's Gael Givet on Boxing Day
'Kenwyne has had one or two issues which people don't know about - there are lots of things that go on with players that affect them - but he is a great lad and will be fine.'
Pulis could not hide his delight at his side's win over Rovers, whose coronation of new boss Steve Kean turned sour and resulted in his side being booed off at the final whistle.
The main man: Stoke boss Tony Pulis
After a first half notable only for Matthew Etherington's astonishing point-blank 14th-minute miss, Stoke turned up the heat and went ahead six minutes after the re-start.
Huth headed home the opener when he blazed in front of a static Rovers rearguard to angle Etherington's corner into the net, then Robinson denied both Jones and Dean Whitehead.
Rovers, who struggled to carve clear chances throughout, came close through youngster Grant Hanley who headed straight at Asmir Begovic.
Then to compound the agony for Kean, Stoke wrapped up the win in injury time when substitute Ricardo Fuller crossed for Wilson to knock home the simplest of chances.
Pulis added: 'I was disappointed it was 0-0 at half-time. We had a couple of golden opportunities and didn't take them. But in the second half we stepped it up a bit.'
Rovers boss Kean admitted his side had lacked spark and will now turn his attention to convincing a number of his unsettled stars to stay at Ewood Park.
Kean has been locked in talks with defender Christopher Samba who has expressed his desire to leave the club. Samba missed the defeat with an ankle injury.
Kean said: 'Christopher would have played [if fit] but he wouldn't have been captain because at the moment he is looking to possibly get away from the club.
'Until he can come back and say he is happy to stay I think we'll look elsewhere in the club. He would have played but he failed a fitness test today.'
Huth and Wilson hand Kean a baptism of fire as Stoke claim winOn-loan winger Pennant in talks for permanent Stoke moveSTOKE CITY FC