Leander Dendoncker scored 15 minutes from time, sending the Molineux faithful into raptures, with Leicester City now the only side able to catch Wolves in the battle for seventh.
Dendoncker guided Matt Doherty's cross past Sergio Rico to earn Wolves a third successive win, ruining Fulham's recent run of clean sheets in the process.
Wolves are now six points better off than Leicester, which has two games in hand, the first of those away to Manchester City this week.
Qualification for European football is not only dependent on the seventh position, though, with Wolves also hoping if Pep Guardiola's can beat Watford in the FA Cup final.
Meanwhile, Harvey Elliott became the Premier League's youngest ever player after coming on as a substitute for Fulham at the age of 16 years and 30 days.
The forward, who made his Cottagers debut in a 3-1 Carabao Cup win at Millwall earlier this season, replaced Andre-Frank Zambo Anguissa in the 88th minute.