Magpies head coach Bruce changed both personnel and system as he attempted to bring greater creativity to his team after they were unable to score against Norwich, Arsenal and Crystal Palace.
The Clarets extended their unbeaten league run to six games with another resilient display at St James' Park.
In his search for greater fluency, Bruce made a raft of changes, replacing the suspended Valentino Lazaro with Javier Manquillo and drafting in Matt Ritchie, Isaac Hayden, Jonjo Shelvey and Dwight Gayle in place of Fabian Schar, Nabil Bentaleb, Sean Longstaff and, somewhat surprisingly, Allan Saint-Maximin – arguably his most creative player.
Gayle saw an 18th-minute shot blocked at source after Joelinton had cut inside impressively from his wide left berth to put the Clarets' defence under pressure.
Keeper Martin Dubravka needed every inch of his frame to claw away Jeff Hendrick's teasing 22nd-minute attempt with the visitors pressing, but James Tarkowski bravely blocked Shelvey's drive with his head as play switched rapidly from end to end.
Pope got down well to collect Miguel Almiron's effort after he had collected Ritchie's pass and Ritchie headed wide after meeting Gayle's cross from the left.
Almiron saw his shot blocked just before the break, after Shelvey's scuffed volley had been repelled, and Ritchie and Gayle both went close from the two corners which followed, but Burnley held out to reach the break with their clean sheet intact.
Shelvey curled a 51st-minute free-kick well over Pope's crossbar and it was Newcastle who continued to enjoy the wind in their sails.
Substitute Chris Wood could not hit the target after climbing high to connect with Dwight McNeil's inviting 65th-minute cross, but Gayle was similarly inaccurate with an acrobatic effort from Almiron's delivery seconds later.
There were cheers from the home crowd when Saint-Maximin was called from the bench to replace Joelinton with 12 minutes remaining, but it was Ritchie who almost broke the deadlock with an 81st-minute piledriver which flew just wide.
Saint-Maximin forced Pope into a solid save with a drilled effort and Almiron's thrilling surge into the box was ended by Charlie Taylor in a high-octane, but ultimately fruitless finish.