Newcastle went on the attack early and had an early chance of Connor Russo’s throw, but Askey and Jack van der Laan both failed to make the connection.
Russo, playing on the wing, was finding plenty of space on the right, and twice in quick succession put crosses in, with both going over the bar.
Stafford then came forward and Alex Kiwomya was inches away from opening the scoring, just failing to reach an excellent cross across the goal.
Russo then followed that up with a close-range header that forced Stafford keeper Cameron Belford to make a sharp save. From the resulting corner, it was Jake Dennis’ turn to miss the ball with his attempted header in a dangerous position.
However, from that point, Stafford began to force their way into the game, with Ntumba Massanka heading wide from a perfect position.
But Stafford could not fashion a clear goal-scoring opportunity, with a couple of long range shots fired over the best they could show.
Instead, with the half coming to a close, Newcastle came forward, and Russo’s throw was right in the mixer, and Askey headed in through the chaos.
Stafford came out for the second half eager to equalise but quickly found themselves further behind.
Jack van der Laan muscled Stafford off the ball and released Russo, whose blocked cross fell for Ethan Vale, who delivered a perfect cross for Lovatt to head home.
Now two goals down, Stafford rallied and dominated most of the rest of the game, but failed to land any telling blows to Newcastle.
Newcastle keeper Joe Slinn had to be sharp to push a shot over the bar, as Stafford tried to pin the visitors in their own half.
Stafford had a series of corners and long throws from their captain Tom Tonks which gave them plenty of possession in the Newcastle box.
However, some brave goalkeeping from Slinn, and key interventions by Askey, Dennis and Vale repeatedly diffused the danger.
Stafford was displaying some good build-up play, but could not find a good chance to shoot, with Kiwamya firing two long-range shots over.
Instead, Newcastle was able to run the clock down, and hold out for their second clean sheet of the season.
The Second Qualifying round draw is on Monday 5th September and fixtures will be played on 17th September.