Their new signing from Scarborough, Neil Bishop, made his City debut in a 4-4-2 formation and was quickly showing his worth earning an early free-kick which saw Andy Bishop have a 20-yard effort saved by Nikki Bull.
Mark Convery was then narrowly wide with a snap shot following a fine four-man move.
Visitors Aldershot went ahead against the run of play on 16 minutes. Ryan Williams cut into the box and fired in a curling effort which Jonny Dixon glanced beyond keeper Chris Porter.
City should have been back on level terms inside 60 seconds, but Emmanuel Panther somehow contrived to fire over from 12 yards with the goal gaping from Andy Bishop's clever pass.
Clayton Donaldson was unlucky with a spectacular overhead effort from Nathan Peat's cross which Bull took under the crossbar.
City were launching wave after wave of attacks and Donaldson set strike partner Andy Bishop free from halfway, but his run ended when Lewis Hamilton appeared to haul him down inside the box but nothing was given.
Donaldson went close from a tight angle before he beat two defenders and passed to Convery who struck a fine equaliser from the edge of the box.
The Minstermen could have gone ahead soon after when Donaldson was put clean through, but keeper Bull saved brilliantly as the striker tried to round him.
City started the second period as they ended the first and were rewarded with two goals in the space of three minutes.
Star performer Neil Bishop released Convery with a superb pass and the cross from the right was bundled home at the far post by Andy Bishop for his 15th of the season.
The Shots gifted City a third when Porter's punt downfield was missed by two defenders and Donaldson had the simple task of stroking the ball past Bull from 12 yards.
City tired in the closing stages and Williams scored a superb goal to raise the home supporters' anxiety levels.
His sweetly struck free-kick cleared the defensive wall and beat Porter's despairing dive, but City held on for the three points.