City came closest to scoring a winner when hitting the post through Eros Pisano, but in the end the sides were made to settle for a point apiece in the West Country.
The home side enjoyed the first half's best chances, though, forcing opposition boss Steve Bruce to revert from a three-man defence to a back four midway through.
For all Bristol's possession in dangerous areas they could not do a great deal with it, however, and when Villa wrested back control of the match they should have edged in front.
On-loan midfielder Onomah, who was wayward with a rash attempt in the first half, fared better early in the second when testing Fielding at his front post.
The sides continued to cancel each other out, until Bristol won a free kick right on the edge of the box an hour in which Villa failed to deal with.
Villa were level just over four minutes later thanks to a slice of luck, as Onomah's latest shot took a heavy deflection off Pack and looped over the reach of Fielding.
Hourihane was denied the chance to continue his fine scoring run when his short was blocked in front of goal, while Joe Bryan had a header stopped by Johnstone.
City, without a win since the opening day of the season, were the side looking the more likely to bag a winner as Pisano's miscued cross needed a touch from Johnstone onto the crossbar 13 minutes from time.
There was to be no way through for either side in the remainder, though, meaning a third successive league draw for the Robins, while Villa have just five points from the first 15 on offer.