Aberdeen took the lead after 13 minutes when an Andrew Considine cross was headed home by Stewart. That was how it stayed until seventeen minutes from time, when Padro Moutinho broke from midfield, outstripping Sven Baas before chipping the ball delicately over the head of Jamie Langfield.
With five minutes remaining, the Dons restored their advantage when a long David Donald throw was back-headed by Stewart to substitute Bagshaw, who drilled a fierce shot past Alan Ferguson.
On the stroke of full-time, Aberdeen made sure of the points when Stewart was brought down iside the area by Ferguson. The former Airdrie youngster took the kick himself, making no mistake to complete the scoring.
Stewart has now scored 7 goals in his last 5 games for the reserves.