Leigh scored three tries in the first 16 minutes to lead 16-0, with Anthony Bate, Tommy Goulden and Steve Maden all claiming tries before the visitors really had a chance to settle.
To their credit, the City Knights tightened a few things up and then started to work their way into the game as James Ford fired a pass wide for Dougie Flockhart to sweep in at the corner.
Tom Carr goaled superbly and the visitors were desperately unlucky moments later when a good attack was disrupted by Leigh and the timely intercept from Martyn Ridyard saw the hosts advance down the ground with Johnny Pownall outpacing the last two defenders for the score.
Just before the break, the York defence cracked again as Stuart Littler stretched over and the pressure was building early in the second half when Simon Finnigan touched down after just three minutes.
Credit to York, they again wrestled control away from Leigh with a smart reversal from Jon Presley giving Ed Smith his second try of the season.
The Centurions responded with quick tries from Maden and a quicksilver effort from Gregg McNally before York upped the tempo in the last 20 and chased an unlikely bonus point, eventually falling short despite fine scores from Flockhart again and youngster Gregg Minnikin.
Leigh: McNally, Maden, Littler, Gardner, Pownall; Ridyard, Nicholson, Ostick, Beswick, Bate, Finnigan, Goulden, Hopkins. Substitutes: Penkywicz, Thornley, Bullock, Duffy.
York: Ford, Minnikin, Latus, Briscoe, Flockhart; Carr, Presley, Freer, Lee, Aldous, Scott, Smith, Picketts. Substitutes: Brining, Sullivan, Potter, Mallinder.
Referee: Matt Thomason (RFL).
North Wales Crusaders thrashed Gloucestershire All Golds 58-16 in Kingstone Press Championship 1.