Mavrias scored after just five minutes but it was far from a comfortable afternoon for the Premier League side as they were made to work by their spirited non-league opponents.
Only Lee Cattermole was retained from the Sunderland side that knocked Manchester United out of the Capital One Cup as Gus Poyet tested the depth of his squad, which meant debuts for January signings Oscar Ustari and Santiago Vergini and a first start for midfielder El-Hadji Ba.
The Black Cats were in front with just five minutes gone when Harriers defender Josh Gowling fired his attempted clearance straight at Mavrias, who gratefully accepted the opportunity to open his account at the Stadium of Light.
But as the home fans settled down for what they hoped would be a regulation victory, Kidderminster very nearly dragged themselves back into the game within five minutes.
Emanuele Giaccherini and Cattermole combined to serve the ball up to Michael Gash, who ran in on goal before unleashing a right-foot shot which very nearly squirmed through keeper Ustari's dive.
Gash, playing as a lone frontman, battled gamely to put Vergini and central defensive partner Modibo Diakite under pressure, but Ustari was otherwise untroubled with Sunderland dominating possession.
They prospered in particular out wide, where full-backs Ondrej Celustka and Valentin Roberge linked well with midfielders Sebastian Larsson and Mavrias to pin Kidderminster back.
However, they created few chances of note as a rather drab first half limped towards its conclusion.
Cattermole forced a rare save from keeper Danny Lewis from 30 yards and Giaccherini shot wastefully wide from a promising position inside the penalty area before blazing a later effort high over.
Roberge saw another attempt from distance drop on to the roof of the net with the aid of a deflection as Lewis found himself largely untroubled.
The keeper might have been in serious trouble within two minutes of the restart when the ball dropped to Ba on the edge of the box, but the Frenchman's scuffed shot trickled into his arms.
However, with captain Kyle Storer and Jack Dyer starting to get a grip in central midfield, the visitors began to string passes together to lay a foundation for something more progressive.
Lewis was troubled on the hour when Vergini unleashed a 30-yard effort which he could not hold, although the element of surprise at the ferocity of the shot was perhaps partly responsible for his discomfort.
Ba floated a curling 64th-minute attempt over the angle of bar and post as Sunderland attempted to restore a measure of control, and Poyet introduced Craig Gardner and Fabio Borini in place of the ineffective Giaccherini and Ba in an attempt to aid that process.
In the meantime, Storer had been fortunate to pick up only a yellow card for an ugly challenge on Roberge.
Borini saw a close-range shot charged down with the home side looking belatedly to kill the tie off, but it was all a little limp as the game crawled towards its conclusion with little urgency.
However, Ustari found himself in the firing line twice within seconds as full-back Danny Jackman drilled wide and then substitute Freddie Ladapo blasted an 88th-minute thunderbolt inches past the far post.
But it took a remarkable injury-time block by right-back Lee Vaughan to prevent Borini from extending the lead in a finish which had little in common with much of the rest of the game.