Sheffield Wednesday eked out another point in their bid to beat the drop, but manager Paul Sturrock will consider it two points dropped against shot-shy Burnley.
The Owls dominated possession either side of the break, but could not find that killer touch to follow up last week's 3-1 win at Wolves with another three points.
Burnley improved slightly in the second period, but had set their stall out early on in front of a near 25,000 crowd at Hillsborough.
Owls boss Paul Sturrock made just one enforced change to the side that started last week at Wolves with John Hills in at left-back for knee injury victim Peter Gilbert, while Burnley counterpart Steve Cotterill also named an unchanged starting line-up.
An uninspiring open quarter was punctuated by just one effort on goal and that came from Sheffield Wednesday via Chris Brunt, who headed wide when well-placed six yards out.
Wednesday fans eager to see their side with their tails up after last week's stunning success at Molineux were left disappointed. The first shot on goal - Owls striker Burton O'Brien miscued left-footed from 12 yards - came in the 27th minute.
But Marcus Tudgay, two-goal hero at Wolves, forced Brian Jensen into a fine save soon after, the Burnley goalkeeper turning away his shot from the edge of the penalty area.
Glenn Whelan's 20-yard shot was blocked by Burnley defender Phil Bardsley 10 minutes before the break and Brunt was wayward with a long-range strike, while Burnley failed to muster a single effort on goal.
Wednesday's on-loan defender Mikkel Bischoff failed to show after the break due to injury, handing Lee Bullen another substitutes' appearance, but the pattern of play was much the same, Wednesday dominating possession and probing; Burnley keeping shape and happy to defend from the front.
Hills' speculative second-half shot from 35 yards that drifted wide was all the Owls had to show for bossing play up to the hour-mark.
But from there on the game began to open up. Burnley defender Frank Sinclair headed Alan Mahon's cross narrowly wide and following Brunt's 20-yarder at the other end, visiting striker Andy Gray forced Scott Carson into his first save from a raking drive the England World Cup hopeful parried away for a corner.
Mahon was making inroads down Burnley's left and another cross was headed wide by fellow midfielder Chris McCann.
Tudgay and Michael Ricketts traded 25-yard shots, the latter's held by Carson, while Yoann Folly tested Jensen from similar distance and O'Brien also blazed wide from outside the area.
Owls winger Jon-Paul McGovern replaced Deon Burton with seven minutes to go to make his first appearance in an injury-ravaged season since November last year, but in the last seven minutes failed to make it a dream comeback.
Teams
Sheff Wed Carson, Bischoff (Bullen 45), Coughlan, Hills,Simek, Folly, Whelan, O'Brien, Brunt (Best 66),Burton (McGovern 83), Tudgay.
Subs Not Used: Adamson, MacLean.
Booked: Simek.
Burnley Jensen, Sinclair, Duff, Bardsley, Harley, Mahon,James O'Connor, Branch, McCann, Ricketts (Spicer 82), Gray.
Subs Not Used: McGreal, Hyde, Elliott, Lafferty.
Booked: McCann.
Att: 24,485
Ref: G Laws (Tyne & Wear).