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They were without regular centre back Jamie McCombe who was suspended and it showed late on when they came under non-stop pressure from Ian Holloway's battlers.
Maynard's strike just short of the half-hour was as sublime as an earlier miss when he failed to turn in a simple tap had been inexplicable.
Running in from the left he had turned in the box with his back to goal as Marvin Elliott sent a downward header into him. With central defender Alex John-Baptiste right behind he had no room to turn but an over-head kick wrong footed the defenders.
His goal came barely ten minutes after he had run an intelligent chip and the Costa Rican striker Alvaro Saborio wide of the far post.
Inspired by Evander Sno who is on a season-long loan from Ajax, City had already passed up two other scoring opportunities but found they had no time to relax.
Blackpool opened up their game as they chased an equaliser and it was nearly there as Elliot lost out on mid-field to Hameur Bouazza.
He ran in to set up a header for Ben Burgess which was one handed over the bar. The visitors tried to tighten up on Sno at the start of the second half but were quickly undone by a tactical switch.
Alvaro Saborio was replaced by Danny Haynes and in little over five minutes Haynes had the points virtually sewn up as he drove an astute back heel from Maynard into the bottom right hand corner.
Elliot could have made it three moments later; sparking Blackpool's manager Ian Holloway into a triple change.
Seasiders sub Billy Clarke produced an outrageous shot from 35 yards to stoke up the pressure on City as Blackpool swarmed into the final third but couldn't get a shot beyond the Brazilian keeper Adriano Basso.