Former Crewe striker Maynard notched his sixth goal in his last seven games as the Robins continued their impressive start to the Championship season.
Leon Best had given the Sky Blues a deserved lead in the first half and Chris Coleman's side spurned several opportunities to secure their first win against the Robins since August 1979.
But Gary Johnson's side regrouped after the break and deserved their point.
Sky Blues winger Michael McIndoe was eager to prove a point to Gary Johnson having left been sold by the Robins in the summer and the Scotsman flashed an early shot wide.
Martin Cranie forced Dean Gerken into a save after 10 minutes with a vicious drive from just outside the penalty area.
And Clinton Morrison wasted a glorious chance to put Coleman's
side in front whe he headed wide from close range but they were ahead after 17 minutes.
Full-back Marcus Hall swung over a cross from the left and Best was on hand to nod home from just six yards out.
The home side were dominant and Gerken tipped McIndoe's free-kick round the post before Best's acrobatic overhead kick flashed over the bar.
Gerken was called into action once again to keep out a header from the dangerous Best but the Robins almost equalised against the run of play when Jamie McCombe forced Keiren Westwood to make a sharp save.
Alvaro Saborio had a chance mark his Robins debut with a goal but the Costa Rica striker was denied by Westwood.
Former Crystal Palace striker Morrison was presented with an opportunity to make it 2-0 nine minutes before half-time but fired over the bar.
And Coventry were made to pay for their profligacy when Saborio passed to Maynard, who fired a thunderous shot which flew past Westwood and went in off the bar.
Saborio had another opportunity to open his account for the Robins two minutes later but dragged his shot wide.
And Sky Blues keeper Westwood had to be at his best to tip Cole Skuse's header round the post 61 minutes in as the visitors went in search of a winner.
The visitors looked the more likely to secure all three points and McCombe should have done better with a header with 20 minutes remaining.
Coventry were well and truly on the back foot and new signing Evander Sno could have won it for the Robins, but fired wide with seven minutes remaining.