After a stop-start first half, Clitheroe put on their usual power show in the second, but gave their fans a few nervy moments at the end.
Brad Knox had been first to show and stung the keeper’s hands within the first two minutes.
On 17 minutes, Danny Brady was unusually beaten for pace and Chris Thompson had to pull off a smart save.
One minute later, Dimitri Tuanzebe threaded a ball through the defence for Kurt Willoughby to run on to and score.
The tempo was increasing, and on 22 minutes, Brady had a trademark charge down the pitch, and picked out Alex Newby, who blasted narrowly over.
Five minutes later, the defence opened up in front of Tuanzebe, who passed to Newby, who again drilled it over.
Thereafter, the rest of the half produced few further chances.
The Blues went up a notch in the second half, and on 52 minutes, Willoughby hung a cross in from the left, only for Brad Carroll to head against the bar
Three minutes later the lead was doubled, as Newby skipped down the right and could have gone on himself, but unselfishly chose to lay the ball to Tuanzebe, who made no mistake.
Barely had the game re-started than Clitheroe fell for the sucker punch, as a burst down the left saw a cushioned shot from Stephen Lewis beat Thompson.
However, this side is made of sterner stuff.
On 64 minutes, a great burst down the right by Newby saw him go right to the byeline and pull a cross back, but Ryan Cattermole could not get his shot off.
On 71 minutes, Willoughby outmuscled his marker, pushed the ball 40 yards past him, advanced on goal and drew the keeper, and just when the crowd thought he had done too much, he dragged it back and leathered it home.
Carroll and Newby combined well minutes later, but with no end product.
With seven minutes left, in a defensive melee in the Blues box, Cattermole was harshly adjusted to have raised his boot as he hooked the ball clear while facing goal.
Lewis converted the penalty and almost uprooted the stanchion at the same time.
As the game moved into injury time, the limp away attack suddenly went up a gear, with Thompson saving at the foot of his post and a pile driver skimming the bar.
When the whistle went, the relief was palpable, but this was a fully deserved three points.
Clitheroe: Chris Thompson, Robbie Bromley, Ryan Cattermole, Gareth Roberts, Danny Brady (c), Dylan Smith, Brad Knox (Joe Mitchell), Brad Carroll, Kurt Willoughby, Alex Newby (Mo Cham), Dimitri Tuanzebe (Johnny Hession). Subs: Joe Mitchell, Mo Cham, Johnny Hession. Not used - Andrew Hill, Ollie Stirzaker