Meulensteen had witnessed Fulham throw away a lead in their 2-1 defeat to Tottenham in his first game in charge in midweek.
But the hosts never looked in danger of succumbing to another comeback in what was a comfortable win over Paul Lambert's men on Sunday.
Steve Sidwell scored midway through the first half to give Fulham the lead, which was extended nine minutes later when Dimitar Berbatov scored just his second Premier League goal of the season from the penalty spot.
Both sides created opportunities in an exciting contest, but it was Fulham who were full value for a triumph that ends a run of six Premier League games without a win.
On-loan striker Darren Bent missed out for Fulham as he was prevented from playing against his parent club, while Sidwell came in for Pajtim Kasami in midfield.
Christian Benteke returned to the Villa team as one of three changes made by Lambert, with Chris Herd and Andreas Weimann also named in the starting XI.
Fulham made the better start to proceedings and only the fingertips of Brad Guzan prevented them from taking the lead - the Villa goalkeeper showcasing excellent reflexes to keep out Berbatov's header from Alexander Kacaniklic's corner.
Villa were a danger on the counter-attack and Benteke spurned their first chance as he nodded wide from Gabriel Agbonlahor's delivery.
The Belgian striker proved to be Villa's greatest attacking threat as he was denied by a good save from Maarten Stekelenburg following another good move from the visitors.
Lambert's men were almost made to pay for Benteke's profligacy, but the awareness of Nathan Baker kept them on level terms, the defender clearing Kacaniklic's goal-bound effort.
However, after 21 minutes Meulensteen's side did find the breakthrough when Sidwell cleverly hooked the ball over Guzan and into the bottom corner following good work from Ashkan Dejagah and Giorgios Karagounis.
And just before the half-hour mark the hosts' lead was doubled, Berbatov coolly converting from 12 yards after Kacaniklic had latched on to his ball over the top only to collide with Leandro Bacuna, with referee Mike Dean pointing to the spot.
Fabian Delph and Berbatov both went close in what was an open first half, but it was Guzan who continued to be the busier of the two goalkeepers, as he produced a fine save to deny Philippe Senderos seven minutes into the second period.
Villa struggled defensively throughout the game and they should have fallen further behind when John-Arne Riise headed against the post from Karagounis' cross after 65 minutes.
Riise provided Villa with another scare with a fierce long-range drive in the closing stages before the visitors were denied a late shout for a penalty when Agbonlahor went down, encapsulating their lack of fortune on a frustrating day for the Midlands club.
