Of the two sides relegated from the Premier League last season, Wolves had enjoyed the better start, with the Hammers picking up just two points from their opening three league games of the campaign.
But a stunning strike by Mukasa into the top corner to open the scoring got West Ham back on track as Nuno Espirito Santo secured a much-needed win against his old club.
Jarrod Bowen netted his first league goal of the season from the penalty spot to double the home side's lead before Marshall Munetsi pulled a goal back for Wolves.
Mukasa's deflected effort and Konstantinos Mavropanos's strike added to the West Ham lead before the Greek defender put it into his own net to round off the scoring.
Victory propels West Ham up the table to 11th, while Wolves sit third.
Swansea beat Watford 2-0 to go top thanks to goals from Eom Ji-sung and Adam Idah.
Southampton's charge up the table despite beginning the season with a four-point deduction for spying at the end of last season was halted in a 1-1 draw at Birmingham.
Keven Schlotterbeck nodded Saints in front, but August Priske secured a point for the Blues in the second half.
Bristol City won 3-1 at bottom-of-the-table Preston to climb into fifth, while Sheffield United edged out Bolton 3-2 thanks to Romelle Donovan's stoppage-time winner.
