Sako's first-half strike condemned the relegated Cottagers to a third straight defeat and left them one place off the foot of the table on goal difference.
Sako could even afford to miss a stoppage-time penalty before manager Felix Magath trooped off to chants of 'Felix Out'.
Magath pleaded before the match for the fans to be patient with his young team - he made five changes to the side beaten by Millwall at the weekend and started with six players aged 21 or younger.
Wanderers, by contrast, are a settled, well-organised side who ran away with League One last season and look capable of making light work of the Championship.
They tore into Fulham from the off, with Dave Edwards flashing an early shot across goal and wide and Jesse Joronen having to charge out of his goal to save at the feet of Rajiv van la Parra.
But home keeper Joronen was beaten after 15 minutes when Scott Golbourne's low corner was dummied by Edwards and allowed to run all the way to Sako, who drilled it into the bottom corner to open his account for the season.
Fulham tried to respond and Konstantinos Stafylidis fired narrowly over and then put in a dangerous cross which Tim Hoogland could not get a clean header on.
But they almost found themselves two down before the interval when Wolves skipper Danny Batth got his head to Sako's free-kick only to nod the ball inches wide.
Magath's response was to throw on another youngster, Moussa Dembele, and the 18-year-old almost made an instant impact with a low shot which Carl Ikeme tipped around his post.
But with Ross McCormack again isolated up front - the £11million striker resorted to coming back and collecting the ball from his centre-halves during the second half - Fulham rarely threatened an equaliser.
The Scot's one sight of goal arrived just before the hour mark and his drive from the edge of the area was always rising as it cleared Ikeme's crossbar.
Instead it was Wolves who always looked like adding to their tally, with Matt Doherty and Batth both missing the target with close-range headers before Sako blew their best chance in stoppage time, hitting the post with a penalty after Cameron Burgess tripped Nouha Dicko.