But Luke Varney drilled home 15 minutes from time to grab a deserved share of the spoils for Wednesday, whose squad was ravaged by a virus during the week.
In the second minute Bristol's Dean Gerken was the first keeper to be forced into action as he parried a Tommy Miller effort on the angle from 12 yards.
Marvin Elliott had a great chance to give City a 12th minute lead, but his header from close range was impressively tipped around the post by Wednesday stopper Lee Grant.
With half an hour gone, City's former Ajax midfielder Evander Sno crossed to Maynard, who shot on the turn to bring a sharp save from Grant down low to his left.
Wednesday started to gain the upper hand 10 minutes before half-time and Jermaine Johnson was at the heart of most of this good work.
In the 36th minute he fizzed a 25-yard drive wide following good work by Varney.
Moments later Marcus Tudgay presented Varney with a gilt-edged chance but the striker could only shoot tamely at Gerken.
Johnson continued to torment and four minutes before the break he cut in from the right flank to find Tudgay in the area, but the former Derby man was crowded out in a good position before the could get his shot away.
The hosts began the second half with renewed vigour and they took the lead in the 59th minute.
Shortly after Tommy Miller had hacked off his own goal line when Wednesday failed to clear a Paul Hartley corner, the ball was again pumped into the visitors penalty area and Maynard found space to slot his second goal of the season past Grant.
City were now in the ascendancy and a wonderful solo run from Sno ended with the Dutchman unleashing a rasping shot narrowly over the bar.
With just over 20 minutes remaining Gerken prevented what appeared to be a certain Wednesday equaliser.
The home side failed to clear a dangerous Darren Potter free-kick and the ball fell to substitute Leon Clarke whose goal-bound effort was scooped impressively away from the bottom corner by Gerken.
But he was helpless when the equaliser came in the 75th minute. Tudgay released the hard-working Varney who slammed home a thunderous drive from 25 yards
Moments later Varney almost gave Wednesday the lead when Clarke found him on the left hand side of the penalty area, but Gerken did well to tip another well struck shot around the post.
Sno threatened once more from range with five minutes left, but Grant was equal to his viscously swerving effort.
In the final minute a delicious chip from Clarke was diverted from goal by a back-pedalling Gerken to preserve a point for City.