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Roy Hodgson's side leapfrogged West Ham, who host Liverpool in Saturday's late game, into seventh position in the Premier League and will fancy their chances of holding onto the last European spot.
The west Londoners were much too strong for fast-fading Villa, who stay in fifth place despite extending their woeful run to one win in 11 matches.
Danny Murphy's early penalty had given Fulham the lead at Craven Cottage and, although Ashley Young equalised for Villa soon after, it was Kamara who turned on the style after half-time with two goals in 14 minutes.
Villa's Gabriel Agbonlahor had the first chance when he met John Carew's header with a shot that flashed over.
Fulham replied when Erik Nevland headed Paul Konchesky's cross straight at Brad Friedel.
It was Hodgson's team who took the lead in the seventh minute when James Milner was adjudged to have fouled Kamara inside the penalty area and Cottagers captain Murphy stepped up to stroke the spot-kick past Friedel.
Nevland should have increased Fulham's lead in the 11th minute but the Fulham striker failed to hit the target from just inside the penalty area.
The Norway striker was left to rue that miss as Villa drew level in the 14th minute when a Gareth Barry cross was glanced on by Carew and Young was on hand to slot home.
Fulham went close to going ahead again in the 31st minute when Kamara's shot was deflected over by Stiliyan Petrov.
On the stroke of half-time Agbonlahor sprinted from one penalty area to the other before crossing for Young, whose shot forced Mark Schwarzer into a fine save.
But Fulham took complete control after the break. They scored in the 46th minute when Luke Young's attempted clearance was charged down by Kamara and the Fulham striker despatched an angled drive beyond Friedel from 18 yards.
In the 52nd minute a Konchesky free-kick found its way through the Villa defensive wall but Friedel dived low to his right to prevent Fulham going further ahead.
Kamara made it three for Fulham with his second goal of the game on the hour. A corner from Murphy was headed down by Brede Hangeland and Kamara supplied the finish with a clever backheel.
Villa had run out of ideas and Ashley Young's woeful shot late on summed up their lack of belief.
