The Robins rattled the woodwork after only 12 minutes when Phil Jevons struck a free-kick from 25 yards that crashed back of the left-hand post.
After a howling mistake against QPR in midweek, Mark Goodlad was caught out again in the 14th minute when his attempted clearance to prevent a corner kick fell directly into the path of Jevons.
However, it was former Vale player Steve Brooker who got the chance to shoot but his goalbound effort was neatly dealt with on the line by Vale captain George Pilkington.
Both managers had to re-think their attacking options after 21 minutes when strikers Brooker and Akpo Sodje were forced to the sidelines with seemingly similar injuries.
The Valiants managed their first piece of good play four minutes later when impressive link-up play around the edge of the box set up Danny Whitaker but his shot never troubled Adriano Basso.
Bristol City opened their account on the stroke on half-time when Scott Brown punished Vale's inability to hold onto possession by floating an impressive 30-yard shot over Goodlad.
The home side wasted no time in their search for an equaliser and tested the City backline soon after the restart with Jamie McCombe almost heading into his own net from a Danny Sonner free-kick.
Some excellent defending by Louis Carey kept Bristol's lead intact when he shut out Leon Constantine two yards from goal after Pilkington had crafted his opportunity.
Goodlad was kept busy throughout the afternoon and flew into action twice in the 68th minute when he made impressive reaction saves from both Richard Keogh and McCombe to keep the deficit within reach.
The match was put beyond doubt when, after making a superb saving tackle against Scott Murray, Pilkington's second challenge on Jevons sent the ball looping over Goodlad from 15 yards.