The Dolly Blues were below their best but cemented their place at the summit of the Evo-Stik First Division North as Connerton took his tally to 17 league goals for the season.
It was far from straightforward on Tuesday night, the striker heading City in front shortly before the interval on a difficult pitch.
The Blues toiled for large periods though, Simon Wills driving them forward from the middle of the park, and were pegged back on the hour by Yahya Saeed’s close-range finish.
Phil Brown’s side were back in front from the spot five minutes later however as Connerton kept his cool before the in-form front man sealed the match-ball late on.
The game took time to get going in tough conditions, Connerton failing to test Ciaran O’Loughlin as he blazed over Craig Carney’s pull back nine minutes in.
The erratic visitors, down in 17th in the table, played with real pace and power at times and should have gone in front midway through the half but Mike Hale denied Daniel Burns one-on-one after one of many penetrating runs from Jermaine Metz.
The Blues found their feet as the half progressed though, Carney dragging a shot wide just after the half hour with Adam Sumner bringing a sharp save from O’Loughlin 60 seconds later after a neat one-two with Ryan Winder on the edge of the area.
The opening goal arrived on 37 minutes, Carney’s right-wing cross taking a deflection and looping to the back post where Connerton was on hand to head home.
Brown’s side couldn’t build on their advantage after the interval though, Louis Mayers dragging a shot wide from distance the closest the hosts came at the start of the second half.
Radcliffe sensed an opportunity and after building pressure were level with a soft goal on the hour.
Metz broke in on the right side of the area and lifted the ball over the advancing Hale to the back post with Burns knocking the ball back into the danger area for Saeed to convert from close range.
The visitors were only level for five minutes however and gifted City the lead for the second time.
Connerton capitalised on an error from Jacques Kpohomouh before being felled by the big central defender, the Lancaster man picking himself up to send O’Loughlin the wrong way from the spot.
The goal seemed to halt Radcliffe’s resistance, Connerton nearly completing his hat-trick shortly after only to see a header from a Rob Henry cross sail wide.
Timmy Raheem did fire a shot wide 15 minutes from time but it was the Blues who looked the more likely to get the game’s next goal.
Sure enough, Carney’s dragged shot on 83 minutes was nearly converted by Winder at the back post before City sealed the points three minutes later.
Subsitute Billy Akrigg drove at the Radcliffe defence and slipped Connerton in behind who calmly rounded O’Loughlin to ensure it was job done for the league leaders.
Lancaster City: Hale, Henry, Westwood, Mercer (capt), Sumner, Gregory (Birch 71), Wills, Carney, Winder, Mayers (Akrigg 77), Connerton (Kilifin 88). Subs not used: Clark, Hudson.
Radcliffe Borough: O’Loughlin, Metz, Baldeh, Nalatche (capt) (Mbolokele 78), Kpohomouh, Belezema (Jones 22), Burns, Raheem, Saeed (Hill 77), Eislet, Rokka. Subs not used: Zhekov, Oppong.
Star Man: Simon Wills - Connerton got the goals but the midfielder was the heartbeat of City’s performance.