Motherwell's poor run looked in danger of continuing when Liam Fontaine volleyed home from a third-minute corner.
But the hosts were back in front before the 25-minute mark following goals from Mark O'Hara and Campbell.
The latter sealed the points in the 75th minute and substitute Tony Watt added a fourth with the last kick of the ball.
The win extended Motherwell's lead in third spot in the Ladbrokes Premiership to three points following Aberdeen's draw at Kilmarnock.
Hartley was involved as Motherwell equalised in the 17th minute. The defender headed Liam Polworth's deep cross back into the six-yard box and O'Hara lashed home the bouncing ball.
The home fans were paying tribute to fellow supporter Mark Paton, who died last week aged 24, when their team went in front.
Christopher Long's pace was causing County problems and the striker skipped past Callum Morris early in the second half but had a shot blocked from a tight angle with two team-mates free in the six-yard box.
Laidlaw soon made a brilliant save to push Long's six-yard strike on to the post.
Motherwell remained on top and were showing signs of their confidence returning but needed a third to settle the home fans' nerves given their recent run, which included losing late winners against St Mirren and St Johnstone.
The clincher was provided by Long, who was back in the team after his recent red card against Hamilton. The forward beat Marcus Fraser and drove the ball across for Campbell to tap home from six yards.
With a trip to face in-form Hearts coming on Saturday, Stephen Robinson left David Turnbull on the bench following his first appearance since summer knee surgery last week.
Watt provided a classy finish to claim his first Motherwell goal after being played through by Campbell in stoppage-time.