The Citizens have picked up four points from champions Kelty Hearts and Forfar in their last two games and are now gunning for Cowdenbeath at Central Park tomorrow.
Victory in Fife, coupled with defeats for Stenhousemuir and Stranraer, will take City to within touching distance of a play-off spot for a second successive season.
On the contrary, defeat for the Blue Brazil will consign Maurice Ross' men to the Pyramid play-off final against either Bonnyrigg Rose or the winners of the Highland League.
Maybury expects Cowden to throw the kitchen sink in these desperate times but has full belief his players can get the job done.
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"Listen, it was a disastrous start up at Elgin but then we picked up a point against the champions and took all three last week so we're building some momentum," Maybury said. "But with three tough games to go, we've just got to pick up as many points as we can and see if it's enough to take us into the play-offs.
"Cowden have been in really good form and picked up a brilliant win down at Annan last week. They're getting results so we know it's going to be tough. The league is tight and anyone can beat anyone on their day. We've done our homework on them so we're aware of how they work and what they do so we just need to try and combat that. We need to stick to our aims and see if we can get the points that just keeps us ahead of the pack at the moment.
"It's been so nip and tuck where we lost a couple of games and Stenny picked up a few points so there's no one giving an inch. Stranraer are still in the mix too and they and Stenny have to play each other so it's all still so tight. But if we keep picking up the points then we'll finish in fourth.
"The squad is probably as strong as it has been for a while so things are moving in the right direction."