It was the fourth time this season City had been held to a draw after surrendering the lead.
Maynard with his tenth goal of the season and Varney's equaliser from 20 yards gave the game something it had been looking for - a sense of purpose.
It all began brightly enough with Tommy Miller drawing a save from Gerken at the foot of his right post and Varney coming in from the right to smack his shot against the same post.
The flag had gone up for offside, but the importance of it for the Owls was that both attempts had caught defenders on the wrong foot.
Their own backline which had seen seven goals go past them in their last two away games was equally suspect, but Lee Grant pulled off a great deflecting save to stop City going ahead.
From wide on the right Danny Haynes flighted his cross expertly and Maynard's powerful header looked a certain goal until Grant somehow conjured it over his bar.
The game went to sleep then for a long time, home manager Gary Johnson waking it up as he reshaped a non-functioning midfield.
The arrival of former Celtic midfielder Paul Hartley gave City an accuracy of pass they had been missing, while the arrival of Costa Rica World Cup man Alvaro Saborio for Louis Carey gave them added pace.
A striker for a defender was a bold call but it wasn't quite enough to bring them all three points.