Goals from Sam Vokes and Scott Arfield secured a 2-0 win at Turf Moor and push the Clarets in to the top two in the Championship.
Burnley's task of preserving their unbeaten record in 2016 was never going to be an easy task following Neil Warnock's return to management at Rotherham United.
And so it proved. It wasn't the Millers' intention to attempt to out-play the Clarets. Instead the visitors adopted a physicality and awkwardness, slowing down the play, to make life difficult for their hosts.
The early exchanges, in-particular, were extremely scrappy and it wasn't until Sean Dyche's side began to work the ball out wide that any kind of threat was posed in the fixture.
Matt Lowton, one of the club's most economical outlets this term, was the first to expose the away side's back line and when Lloyd Doyley headed the defender's delivery clear David Jones sliced a volley wide.
Greg Halford's long throw was another testing weapon in United's arsenal, forcing the Clarets to retreat deep in to the area, and as one was cleared Richie Smallwood skewed his attempt wide from outside the penalty area.
At the opposite end, Millers skipper Kirk Broadfoot wrestled Michael Keane to the ground from Jones's corner but referee wasn't entertaining the appeals.
A succession of corners saw the Clarets assert more pressure and somehow Stephen Ward failed to flick the ball past Camp from close range after Ben Mee had headed Jones's set-piece back in to the mix.
The pressure finally paid in the 27th minute when the home side countered well, Ward fed George Boyd and the winger was tripped on the turn by Doyley just inside the penalty area.
With Andre Gray and Vokes rotating responsibility it was the Welshman's turn to try his luck from 12 yards out. And the striker made no mistake, slotting low to his left and sending Camp the wrong way to secure his ninth goal of the season.
Moments later, Keane was in the wars and the home support were given their first opportunity to see deadline day signing James Tarkowski in action.
Burnley went close to a second when Broadfoot clipped the ball off the toe of Gray from Ward's exceptional centre, but the Championship's leading scorer stayed alert to head another delightful cross from Lowton against the bar.
Injury to Danny Ward then saw Warnock introduce Grant Ward, with the Spurs loanee scoring a thunderbolt in the reverse fixture at the New York Stadium earlier in the season.
He almost produced similar within minutes, benefiting from Jonson Clarke-Harris's knock down from Camp's clearance but the 21-year-old's arrowing half-volley from 25 yards out dipped just too late to trouble Tom Heaton.
As the curtains came down on the first half Ward moved infield and flicked over the bar with the outside of his left boot.
The second half was just as ugly but the hosts survived a scare to claim maximum points and move in to the division's automatic spots at Middlesbrough's expense.
Burnley pressed from the off and almost extended the lead when Joey Barton's magnificent cross breached United's back line but Vokes, on the stretch, could only poke the ball over the top.
The Clarets goalscorer went close again as the half wore on but Gray, sent clear by Tarkowski's clearance down the right hand side, put too much on his cross and Vokes was unable to convert.
With the away side committing more men forward in hope of salvaging a point the Clarets were able to capitalise.
Again, Gray's pace from Lowton's pass over Broadfoot saw the striker get in behind but the club's record signing delayed his shot and made it easy for Camp with the attempt that followed.
The Millers should've been level shortly after and it could prove a costly miss from Joe Newell in his side's battle for survival.
Frazer Richardson hit the diagonal and the midfielder took the ball in his stride past Lowton but somehow flashed his effort wide of the upright with Heaton rooted to the spot.
Camp denied Boyd from Gray's cross while Vokes's follow up was blocked on the line. However, the Clarets were given some breathing space when space opened up for Arfield from Gray's pass and the midfielder finished well.