Maddison's set-piece was spilled by Sutherland to allow Newton to snap up a simple opportunity.
As Newcastle continued to attack with menace, few would have backed United to regain the lead but Joyce's side showed their character by scoring again. Another Januzaj corner eventually fell to Michele Fornasier, who sensibly fired the ball across for substitute Lawrence to touch home from close range.
Bebe squandered a gilt-edged opening to effectively wrap up the points when he raced clear on Alnwick's goal. The assistant referee's offside flag was rightly over-ruled as the last touch had come off a Newcastle player but, as everybody else stopped, the Portuguese import made a total hash of his finish by smashing a wayward drive.
Bebe was closer to a clincher when hooking a volley wide after a Lawrence free-kick fell to him while Yven Moyo headed inches off target at the other end. United pressed with more conviction towards the end and were relatively comfortable in seeing out the closing stages until Abeid forced a fine save out of Sutherland in stoppage time.
United: Sutherland; Veseli, Wootton, Fornasier, Vermijl; Januzaj (Ekangamene 76), Thorpe, Tunnicliffe, Cole, Bebe (Hendrie 90); Macheda (Lawrence 54). Subs not used: James, J.Pereira.