First-half goals from Steve Sidwell and Dimitar Berbatov, who scored from penalty spot, were enough to give Fulham a deserved win in just Meulensteen's second game in charge.
Villa were far from their best as Fulham took all three points to boost their survival hopes, with the three points lifting them back above Crystal Palace in the table.
Fulham started brightly and they had a penalty appealed turned down on eight minutes when Berbatov appeared to be pushed in the back by Nathan Baker. Seconds later Brad Guzan denied Fulham the opener when he produced a brilliant diving save to push Berbatov's header onto the crossbar.
Villa created the first chance of the game on 12 minutes when Gabriel Agbonlahor picked out Christian Benteke inside the box, but the striker flashed his header wide of the target.
Benteke had another sight of goal four minutes later when he worked some space on the the edge of the box and drilled in a shot which Maarten Stekelenburg did well to push out.
Fulham almost broke the deadlock on 18 minutes when Guzan rushed from his line to block Ashkan Dejagah before the ball broke to Alex Kacaniklic, who saw his follow-up effort kicked off the line by Baker.
The home side made the breakthrough on 21 minutes with Sidwell finding the net against his old club with a goal of real persistence.
Sidwell beat Leandro Bacuna to get on the end of Dejagah's flick into the box and scooped the ball over Guzan and into the net from a tight angle for his third goal of the season.
Fulham won a penalty on the half-hour mark when Berbatov sent Kacaniklic scampering clear with a superb pass and Bacuna collided with the winger inside the box to concede the spot-kick.
Berbatov made no mistake from the spot as he strolled up and coolly sent Guzan the wrong way with a nonchalant effort.
Villa tried to find a way back into the contest and Fabian Delph played a neat one-two with Benteke before flashing his shot right across the face of goal.
Berbatov was really in the mood for the game and he went close again on 37 minutes when he swapped passes with Sidwell on the edge of the box and fired in a shot which forced Guzan into a good save.
Fulham picked up where they left off at the start of the second half and Philippe Senderos had the first chance after the restart when he forced Guzan into a decent save with a header from Kacaniklic's cross.
Giorgos Karagounis then tried his luck from long range just before the hour mark when he tricked his way past a couple of Villa challenges before driving his effort over the crossbar.
Fulham were inches away from making it 3-0 on 65 minutes when Guzan flapped out a cross from Karagounis and Riise got his head on the ball only to see it come off the base of the post.
Villa had strong claims for a penalty six minutes from time when Agbonlahor appeared to be caught by Aaron Hughes inside the box, but referee Mike Dean turned down their appeals as Fulham ran out comfortable winners in the end.