After an uneventful first quarter the Tigers went ahead when Joseph diverted the ball past Bazunu – how much the attacker knew about the goal was debatable after Joe Gelhardt’s header from Lewie Coyle’s cross was pushed away by Saints’ keeper.
Southampton’s first chance of note came eight minutes later when Finn Azaz put Damion Downs through on goal, but the United States striker saw his low effort from the edge of the box slide wide of the far post.
Saints had an excellent spell of pressure in the first five minutes of the second half, but a lack of cutting edge meant only a deflected long-range Jack Stephens strike posed any danger.
A ball from Coyle was again the cause of the second goal as his floated pass was headed across the edge of the box by McBurnie and Lundstram was there to sidefoot home from 10 yards for his first goal since joining from Turkish aside Trabzonspor on a season-long loan.
Still reacted by bringing on Armstrong, Leo Scienza and Cameron Archer as he searched for a goal, but it was the hosts who made the game safe – Ryan Giles’ floated free-kick from the left was headed home by the experienced McBurnie.
McBurnie almost got on the end of another chance a few minutes later before Armstrong made the score respectable as he chested down Ryan Fraser’s pass before swivelling and shooting low past Ivor Pandur.