New striker Gary Fletcher grabbed his second goal in two games and Lincoln finally broke their duck.
Fletcher, signed earlier in the month from Leyton Orient, was first to react when Ben Futcher headed down a long throw in the 21st minute.
The York defence could only watch as Fletcher lashed home a right-foot shot from inside the six-yard box.
York struggled to find the form that earned them four consecutive wins although they almost snatched an equaliser midway through the second half.
Mitch Ward curled in a 25-yard shot which was heading for the top corner until Lincoln keeper Alan Marriott somehow pushed it out.
The ball went straight into the path of York substitute Jon Parkin but from close range he put his header wide.
Disaster struck the Minstermen 18 minutes from time when defender Dave Merris slipped inside his own box while attempting to clear.
As he lay stranded on the ground Richard Butcher took the ball of him and finished with a left-foot shot straight into the bottom corner.
Seven minutes later Marcus Richardson had the ball in the York net again only for his effort to be disallowed for offside.
But Lincoln grabbed a third when Mark Bailey was chopped from behind by Darren Dunning.
Dunning was red carded and from the resulting penalty Paul Mayo sent keeper Mark Ovendale the wrong way.
In stoppage time Ovendale saved York from even further embarrassment when he was quickly off his line to smother a shot from Niall McNamara.
Lincoln manager Keith Alexander said: "We played very well. It was nice to get a win to keep the doom and gloom merchants at bay.
"I thought we won it well. York are a good footballing side but we watched them and always thought we would be the stronger team.
"I didn't think York created many chances but while we were only one goal ahead the game was always on a knife edge." York player-manager Chris Brass, forced to sit out the game through suspension, said: "We only showed glimpses of what we are about.
"We didn't assert ourselves on the game but I think the score flattered Lincoln.
"It was a bad day at the office but we have to take the positives from the game and build on them. If we can do that we will be fine."