Despite reaching the Carling Cup Final, Villa had seen their league form take a slump in their previous four games as they failed to score a goal and only picked up two points.
But Agbonlahor ensured they got back to winning ways with a stunning display which keeps alive their hopes of challenging for a top-four finish.
In stark contrast, Fulham's season is taking a major downward spiral and they could yet face a relegation dogfight if they don't improve their form in the next few weeks.
Villa came close to breaking the deadlock on 33 minutes when Ashley Young crossed for Luke Young whose close-range header produced a superb save from Mark Schwarzer who did well to tip the ball over the bar.
The away side continued to create the best openings and Stiliyan Petrov blew a golden chance to get on the scoresheet on 35 minutes when he was clean through inside the box but fired his shot over the bar.
Villa finally got their just rewards when Agbonlahor fired them into the lead on 40 minutes. Petrov's cross picked out the Villa striker who rose above Chris Smalling in the box and flashed a close-range header past Schwarzer.
It was his first league goal since he netted the winner against Manchester United at Old Trafford in December and could not have impressed Sir Alex Ferguson who was watching his latest new recruit from the stands.
Agbonlahor grabbed his second of the game on the stroke of half-time. Carlos Cuellar played the ball into the England forward and he curled a superb shot past Schwarzer into the corner of the net.
Fulham refused to lie down and almost pulled a goal back on 67 minutes when Smalling's header was kept out by Brad Friedel.
The home side finally had the ball in the back of the net on 76 minutes when substitute David Elm slotted a shot past Friedel but his effort was ruled out for offside.
Villa held on to record a comfortable win which gives them plenty of confidence as they prepare to face Tottenham and Manchester United at the start of February.