The outlook of the game was altered in the 22nd minute when referee Martin Atkinson deemed Everton's Jack Rodwell's challenge on Luis Suarez worthy of a red card.
The visiting Reds failed to make their numerical advantage count during the remainder of the half, with Dirk Kuyt spurning their best chance when his penalty kick was turned wide of goal by Howard after Phil Jagielka had brought down Suarez.
However, 20 minutes from time Carroll struck into the bottom right-hand corner of the net following a cut-back from full-back Jose Enrique.
That advantage was doubled nine minutes from time when Suarez capitalised on a defensive mix-up between Sylvain Distin and Leighton Baines to curl the ball beyond the reach of Howard from close range.
In response Louis Saha shot wide for the Toffees when well placed, while up the other end substitute Steven Gerrard's goal-bound effort was deflected wide by Jagielka.