The Clarets are still without an away win this term but another point from the stalemate against Sunderland at the Stadium of Light has moved them another step closer to safety.
Sean Dyche's side are one of just two clubs in the country not to have claimed a maximum on the road this season - with Leicester City's win over West Ham meaning Rotherham United share Burnley's unwanted record - but the club can certainly take positives from the result.
It was a game that Burnley dominated for large amounts, a huge opportunity to get that monkey off their backs, but in the end they couldn't find the breakthrough that would bring a first top flight win on Wearside since Ralph Coates scored in a 1-0 win at Roker Park in October 1969.
The visitors commanded the centre of the park, were first to every second ball and worked a number of excellent openings in the first half as they looked to further damage Sunderland's plight while enhancing their own position in the Premier League.
The Clarets were gifted an opulence of space in-between the home side's back two banks and they went close to capitalising early on.
The Black Cats were poor;ly positioned defensively when Jason Denayer's headed clearance fell at the feet of Andre Gray, strike partner Ashley Barnes spun off the shoulder to chase the leading scorer's pass and, with Jordan Pickford caught in two minds, the forward went for an audacious finish only to be foiled by the goalkeeper.
David Moyes's men barely posed a threat, with the front three of Adnan Januzaj, Jermain Defoe and Fabio Borini starved of possession, and could only list a couple of half chances in the opening 45 minutes of the fixture.
One of those saw Darren Gibson's rising shot from 25 yards out clear the bar after Seb Larsson's initial effort had been blocked by Michael Keane.
Burnley were moving the ball well as the territory which they ruled grew and grew. Gray was heavily involved once again in their next attack, holding the ball up well before slipping it in to the inside channel for Stephen Ward.
The full back pulled the ball across the six-yard box from the bye-line, awaiting a touch from George Boyd to convert, but the winger went with the wrong foot and failed to connect with the ball.
As the pressure mounted, Scott Arfield guided his free kick wide of the near post after Boyd was fouled by Darron Gibson.
After Barnes cranked his neck to direct Arfield's corner over the bar, the hosts forged two opportunities to sucker punch.
Rodwell's flick from Larsson's delivery was held by Heaton while Gibson, picked out unmarked on the edge of the box from Januzaj's corner, steered over.
That was as good as it got for the Black Cats and they were fortunate not to go in to the break a goal down.
Boyd's sliced shot wide was the least of their worries; the winger missing the target after John O'Shea's headed clearance from Heaton's free kick fell kindly.
It was Barnes who really should have done better in the closing moments of the half. The striker stepped up perfectly to beat the home side's offside trap but somehow diverted Arfield's effort wide of the upright from close range.
The roles, though, were reversed after the break and it was Sunderland who crafted the more genuine openings.
Heaton denied Fabio Borini at his near post after the Italian striker raced in behind Burnley's backline from Gibson's pass, opened up his body and got a shot away.
The England international was then called in to action again, throwing himself to his right hand post to push Januzaj's volley to safety from Jermain Defoe's cross before Larsson side-footed over when well positioned in front of goal once the ball was recycled back in to the box.
While the away side will rue Barnes's failure to convert in the first half, Sunderland will look back on Billy Jones's miss as a huge opportunity squandered.
The flight of Larsson's delivery rendered Burnley's defence redundant and Jones, as the spare man on the far side, looked certain to give the hosts the lead. However, the defender somehow got it horribly wrong and steered his header wide when stooping low to meet the cross.
Sunderland went close again when Januzaj's left-footed drive from 20 yards out grazed the outside of the post and, at the opposite end, substitute Sam Vokes did well to manufacture an opening when stealing possession from Denayer, driving in to the box and firing across goal only for Jordan Pickford to save well.
The final chance of the afternoon fell to the home side but again Borini, without a goal since Boxing Day, was thwarted by Heaton at the near post.