Liam Hatch in his last game for the Bees was given the captain's armband and he should have opened the scoring in the ninth minute. Unmarked, he miscued his header from Nick Nicolau's cross from eight yards.
Barnet paid for that miss midway through the half when Chesterfield went in front.
Jack Lester fed the ball to Rooney and he toe-poked the ball past Lee Harrison in the home goal.
The visitors came close to doubling their lead when Kovacs had a header cleared off the line by Nicolau from Jamie Winter's corner.
Jason Puncheon nearly replied for the home side at the other end but his long-range shot was comfortably saved by Spireites' keeper Barry Roche.
Kovacs had a great chance the double the visitors' lead minutes after the re-start though somehow missed with a close-range header after Harrison had fumbled the ball.
Barnet, though, seemed to have more zip about them. Neal Bishop flashed a shot wide before Adam Birchall saw his shot deflected over after great set-up play from substitute Anthony Thomas.
Although Gregor Robertson should have done better at the other end after a swift counter attack from the visitors, Barnet continued to pile on the pressure though failed to find a finishing touch.
They paid for their missed chances ten minutes from time when Chesterfield doubled their lead.
Harrison failed to collect an in-swinging corner and Kovacs was on hand to fire in the loose ball via the underside of the bar.