
In a low-key encounter at the Towbar Express Stadium @ The Turnbull Ground, Stewart's header before the break separated the two sides on an afternoon of relatively few chances.
The centre-back headed home following a soft free-kick and Lee Bullock and Nathan Haslam's men were unable to muster a response, with Aaron Haswell and Bullock himself, in the side due to a number of defensive injuries, both going close for the Seasiders as they were beaten for the fifth time in a row at the start of the new season.
The first half brought little action of significant note. The best chance for Whitby fell the way of Nicky Walker early on as his powerful strike was tipped behind for a corner by Cameron Belford.
Striker Marcus Giles probed for a gap to hit a shot towards goal in the ninth minute, but barring this and Lewis Hawkins' effort just before the break, there were no real chances for Bullock and Haslam's men.
Shane Bland did well to deny Ntumba Massanka who was played through one-on-one, but he was unable to keep Stafford out with 33 minutes played.
A Stafford free-kick was awarded midway inside the Whitby half, perhaps softly, and the floated delivery from Joseph Dunne found the head of Stewart who headed home into the bottom corner relatively unchallenged.
The town bosses made a change at half-time with Haswell replacing Giles in attack.
The first chance of the second half fell the way of Hawkins, but despite getting a strong connection on the ball with a diving header following Harry Green's cross, Stafford were able to clear the danger comfortably.
Walker and Hawkins combined shortly after, but Belford was able to palm the midfielder's strike to safety before his side again cleared.
There were two great chances for Whitby to equalise late on as Haswell twisted and turned before hitting the post, while Bullock, pushed up front for the final few minutes, was unable to find the net on the rebound as Belford saved with his feet.
Despite their best efforts, Whitby were unable to force a leveller and they were condemned to another narrow defeat.
A frustrating afternoon for the Blues was summed up after full-time when captain Daniel Rowe was shown a straight red card following a comment made to the referee.