The three points — clinched by Joe Austin’s first goal of the season — took Clipstone up two places to 12th.
The win was the perfect preparation for the Cobras’ Boxing Day home clash with near-neighbours Worksop Town (3pm).
On a heavy pitch, Billy Fox’s players showed the necessary desire, inspired by captain and man-of-the-match Richard Patterson.
The Cobras took the lead in the tenth minute when Patterson and Steve McDonnell combined on the left and the latter pulled the ball back to George Milner, who fired into the corner.
However, the advantage only lasted 60 seconds when poor defending gifted Barton an equaliser.
Clipstone conceded a free kick near the area for handball and when a header came back off the bar, static defending allowed Williamson to head in the rebound.
Chances were at a premium as both sides struggled to find a game plan that would work on the heavy pitch.
The Cobras’ Patterson and McDonnell adapted better to the conditions.
In the 21st minute, McDonnell won back possession and set up a shooting chance for Patterson on the edge of the area, but it went straight at keeper Watson.
Patterson then found McDonnell and he produced a great finish, only to be ruled offside.
The injured McDonnell was replaced after half-time by Martin Brissett, who immediately had an impact when a good turn and cross forced Watson to claim the ball at his near post.
The Cobras restored their lead after 48 minutes with a well-worked goal. A corner from the right was flicked on by Patterson to the far post, where Joe Austin headed home his first goal of the season from close-range.
With Jordan Joynson and Milner combining well down the right, the visitors continued to carry the greater threat but were unable to grab the vital third goal their superiority deserved.
After Nathan Forbes shot wide on the hour for the visitors, only a good intervention by Austin denied Barton’s Nicholls.
Cobras’ striker George Milner shot wide before Austin again got the vital touch to preserve the lead in added time, bravely heading a dangerous home corner clear.
Clipstone: Bailey, Paling, Joynson, Austin, Haigh, Shepherd, Milner, Patterson (c), McDonnell (Brissett 46), Fox, Forbes (Ashmore 85).