Tommy Conway's first-half penalty and a string of fine saves from Max O'Leary helped City bag the points.
The hosts made the decisive breakthrough in the 20th minute after Sunderland were caught playing out from the back. Taylor Gardner-Hickman was tripped by keeper Anthony Patterson and Conway sent the No.1 the wrong way with a low spot-kick.
An inspired performance from O'Leary protected the lead and Sunderland will feel frustrated not to have taken something from an impressive display at Ashton Gate.
Head coach Manning said: "Max was outstanding, not just with his saves, but the composure he showed under pressure.
"I've aged ten years watching the game, but I'm delighted for the lads because of the togetherness and spirit they showed.
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