Striker Maynard, who was a target for West Ham and Leicester in the summer, is out of contract at the end of the season and will be sold in January unless he agrees a new one.
But new City boss Derek McInnes is desperate to keep hold of the 24-year-old, and he showed just why with a well-taken double.
Maynard opened the scoring in the 15th minute and struck the winner in the second half after Jay Simpson had briefly hauled Millwall level.
It means City have now picked up 10 points from five matches since McInnes took over, compared to a measly six from their previous 11 outings.
They are also just two points from safety and today's opponents, who are looking over their shoulders again.
McInnes, a former Millwall midfielder, has got the Robins playing some slick football and their opener came at the end of a patient passing move.
When Neil Kilkenny finally slid the ball behind the Millwall defence, Maynard lashed a powerful first-time shot which flew past David Forde and inside the near post.
They could have doubled their lead on the half-hour when Albert Adomah gave Forde the slip and pulled the ball back for Stephen Pearson, but his shot was blocked.
Forde was by now feeling the thigh injury which forced him to withdraw from the Republic of Ireland squad last week and was replaced by Steve Mildenhall before half-time.
Mildenhall will not have thanked Darren Ward for pitching him straight into the action, the defender's woeful backpass forcing him to dive at Adomah's feet.
The Lions had their chances in the first half as well, the pick of which was Brian Howard's free-kick which was headed off the line by City captain Liam Fontaine, with goalkeeper David James motionless.
Millwall were almost caught napping at the start of the second half when Maynard curled a shot over, before Pearson was inches from sliding in Adomah's ball across goal.
But instead they drew level just before the hour mark, although Darius Henderson handled the ball before his cross was touched on by Liam Trotter for Simpson to lash past James.
However, just five minutes later the lively Adomah had the Lions' defence running scared again.
This time Maynard was on hand to tuck in the winner and prove to City they should do all they can to keep him in January.