The home side led at the interval through Christian Atsu's neat finish on 19 minutes but Stoke levelled against the run of play through Xherdan Shaqiri just before the hour.
Lascelles, the hero last week at Swansea, saw his goal-bound header deflect in off Kevin Wimmer midway through the second half to put the Magpies back in front.
Stoke spurned some good chances to level and really should have gained a point in stoppage time as Mame Biram Diouf somehow headed wide of the target.
With Rafael Benitez back in the dugout, it was Newcastle that made a bright start and they went ahead inside 20 minutes. Matt Ritchie's teasing cross was met by Atsu ahead of Diouf and his shot beat Jack Butland in the visiting goal.
Joselu really should netted against his old club not long after but he shot first time and off target from inside the box. From a corner on 35 minutes, Joselu did manage to test Butland, who was equal to it.
Stoke duly punished their hosts after the break for failing to build on their advantage. Shaqiri picked up possession and moved ominously towards goal before curling a low shot beyond Rob Elliott from outside the box just before the hour.
The visitors almost went in front five minutes later, Shaqiri the provider this time but Diouf's downward header unable to beat Elliott.
Midway through the half the home support was enraged when Atsu felt he was fouled in the box but Stuart Attwell pointed only for a corner.
The frustration was short-lived as Lascelles got his head on Ritchie's delivery and the ball found its way into the net off the unfortunate Wimmer.
In the dying embers, Stoke missed two great chances to level. Sub Peter Crouch set up Eric Choupo-Moting but his finish lacked composure while, in stoppage time, Bruno Martins Indi's cross was met by Diouf who somehow did not hit the target.