Jamie Paterson fired Bristol City in front on 60 minutes against a Villa side who had collected two wins and eight goals in league and cup earlier this week.
But Onomah – on loan from Tottenham – benefited from a helpful deflection off Marlon Pack as his 25-yard effort looped in to draw Steve Bruce’s side level just five minutes later.
It was the first time Villa had battled back from behind to draw or win away from home since 2013.
It was a point their performance deserved but they still needed another moment of luck at 1-1 as Bristol City full-back Eros Pisano struck the crossbar.
For Lee Johnson’s Robins it was a fourth successive draw in all competitions despite Paterson netting the opener when a free-kick conceded by former England captain John Terry bounced around the Villa box.
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Villa boss Steve Bruce said: “I’m delighted that we had a response to the awful goal we conceded, although I’m not sure it was a free-kick.
“We’ve had a good week.
“We got our own bit of luck with a deflection but it was a great strike from Josh who, for me, was the best player on the pitch in the second half.”
City manager Lee Johnson was frustrated Terry was not penalised for handball on the edge of the box.
“He moved his arm towards the ball so it was a definite handball,” he said: “I’m frustrated that we didn’t come away with the win. They got a bit deflection for the equaliser, which was spawny.”