The defender’s near post header from a corner was enough to beat Chesterfield at Saltergate, making it eight wins on the road so far that season.
North End had laid siege to the hosts’ penalty box in the closing stages looking to break the deadlock.
Kidd’s goal came from a succession of corners forced in the last few minutes, to the delight of a large PNE away support which had ventured to Derbyshire.
The goalscorer had only been passed fit in the run-up to kick-off, having missed the previous two games with a sprained ankle.
Sean Gregan also needed a fitness test on the pitch before the team sheet was handed in.
North End’s previous game earlier that week had been a 120-minute AWS Trophy clash on a mudbath of a pitch at Hartlepool.
It was a potential energy drainer, but they lasted the course well and finished strongly – showing good fitness levels.
There was an early chance for Chesterfield when former PNE striker David Reeves got clear on goal.
Credit to North End keeper David Lucas, who dashed off his line to save Reeves’ shot with his legs.
At the other end, Michael Jackson sent a header too high, while Mark Rankine and Jonathan Macken got in each other’s way when trying to meet Gary Parkinson’s cross from the right-wing.
In the first 20 minutes of the second half, Preston had to ride out some pressure from the home side.
Lucas saved well from Reeves for a second time, with Kidd and Jackson having to make a couple of timely tackles.
Steadily, Moyes’ men began to take control and more was seen of them going forward.
As the clock ticked into the last 10 minutes, North End forced a succession of corners.
Left-back Craig Harrison, on loan from Middlesbrough, was on flag-kick duty, taking over from Parkinson, who had been carried off with a knee injury.
His first inswinger was headed behind by a panicky defender. The second was nervously bundled over the crossbar by goalkeeper Billy Mercer.
Chesterfield managed to clear the third. But when Cartwright won a fourth on 85 minutes, Harrison again curled it in left-footed to the near post and Kidd met it with his head and glanced it across into the far corner.
PNE striker Kurt Nogan had two chances late on to make things safe, but Mercer saved them both.
The visitors were given a standing ovation off the pitch by their supporters for a difficult job done
PNE: Lucas, Parkinson (Darby 80), Jackson, Kidd, Harrison, Cartwright, Gregan, Rankine, McKenna, Macken (Harris 75), Nogan (Murdock 90).
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