Kenedy's first performance in the black and white stripes did at least give supporters some encouragement despite another winless game at St James' Park.
The Brazilian winger was denied a goal on his first Premier League appearance since last May when Pope tipped his deflected 20-yard shot onto a post.
Kenedy also earned his side a penalty when he lured Phil Bardsley into a crude challenge but Joselu's miss from the spot - a weak effort that Pope saved comfortably - looked costly.
However, the loan signing's energy seemed to galvanise his team-mates and Lascelles' goal, soon after Ciaran Clark was denied by the impressive Pope, was reward for a hard-working performance.
Newcastle's defensive frailties once again surfaced however, as Vokes' header when under little pressure unluckily ended up in the net via Darlow's head.
Burnley arrived on Tyneside on the back of four successive league and cup defeats and without key midfielder Steven Defour, who faces at least two months out with a knee injury.
While it is true Pope denied Newcastle on several occasions, this was the kind of determined performance by the Clarets that has seen them spend the season in the top half of the table.
This late point moves Sean Dyche's side up one place to seventh, leading the way of the teams outside the 'big six'.
Striker Ashley Barnes wasted an inviting chance when the game was goalless and it looked like another defeat was looming when Lascelles struck.
But Darlow's unfortunate own goal, after new signing Aaron Lennon had come on as a substitute, earned the Clarets their 18th point away from home this season.