The Dolly Blues drew first blood with the attempts on goal when Cole Lonsdale struck from range but failed to test Ossett United goalkeeper, Brett Souter.
However, it was Ossett who took control from there, dominating possession and City struggled in the final third.
Ossett piled the pressure on but failed to really test Jack Sims in the Dolly Blues’ goal.
The more the half went on, the more Lancaster grew into the game and there were two minutes of madness 25 minutes in.
A free-kick on the edge of the box for City was whipped in beautifully to the far post and was tapped in, only for it to be ruled offside.
City then attacked straight after when Ryan Winder swung a wonderful cross from the right wing which was fired into the bottom corner, but again it was ruled out for offside.
It’s fair to say it woke City up and they had the game’s best chance when Glenn Steel headed a free kick inches over the bar.
Rob Wilson then caused Ossett further problems with fantastic fast feet down the right wing when he put a super ball across goal which just missed the head of Ryan Winder.
Ossett, however, were keen to remind Lancaster that they were still in it and they went extremely close from a free kick right on half time.
Into the second half and City came flying out the starting blocks.
Winder continued to be a nuisance, his strike from range on the half volley dipping just over the bar.
Shortly after, Simon Wills found space on the edge of the box but dragged a powerful shot well wide. The game then slowed down and it wasn’t until the 76th minute that the next chance was created when Chris Chantler fired one from range for Ossett, but his effort went just wide of the mark.
Immediately after, Winder forced a super save from Souter from a free kick before City fired one off the post from a header coming agonisingly close in injury time.
Finally though, with the last kick of the game, substitute Charlie Bailey came up trumps with a 95th minute winner to dramatically send Lancaster through.