Phil Brown’s side remain nine points clear but Farsley Celtic, with three games in hand in second, kept up the pressure with a 3-1 victory at Clitheroe.
Both sides had penalty claims turned down in the opening exchanges. First Scarborough’s Jacob Hazel went down after an apparent push before Lancaster’s Jacob Gregory was felled under similar circumstances and neither team would have felt aggrieved if either had been given.
Lancaster went ahead in the 20th minute as good work from Gregory led to Louis Mayers bulldozing through a couple of defenders and clattering against the bar with Connerton on hand to ram the rebound home.
Mike Hale was then almost left very, very red in the face as a fizzing Ricky Mercer back pass was controlled but then sliced into the air straight into Hazel’s path.
The striker had time for at least one touch but opted to try and roll into the empty net on the volley only to shin past the post in a massive let-off for the hosts.
Matthew Lucid was well denied by Hale, as was Ryan Winder at the other end by Joe Green. Adam Bolder was then inches away from levelling as his drive skimmed the bar as chances kept coming for both sides.
City got the crucial next goal though with Connerton’s second having a touch of fortune to it.
Captain Mercer rose highest at the far post to head Winder’s corner goalbound and Connerton instinctively tried to flick the ball on and did so via his back.
Lancaster should have been home and dry within the hour. Lucid was forced into action on his own goal line after a Green error with Winder hitting the post at the back stick after Gregory had rolled across goal.
Adam Sumner’s free-kick then split the wall but Green was on hand to palm away, before Tom Kilifin hit wide on the turn and straight at Green when one-on-one under pressure.
For the visitors, Hale didn’t know much about Matty Turnbull’s shot from close range that bounced off the keeper then the bar.
Lancaster will be happy with how generally solid they looked and will have to keep that up as they travel to promotion-chasing Ossett Town on Saturday, having lost to the Yorkshire side at Giant Axe in October.
Lancaster City: Hale, Henry, Sumner, Wills, Steel, Mercer (capt), Gregory (Akrigg), Carney, Connerton, Mayers (Kilifin), Winder. Subs not used: Birch, Clark, Westwood.