The forward's goal earned the hosts a 1-0 win as Nuno Espirito Santo's side rediscovered their form.
It meant Fulham slipped to a fourth straight loss to remain bottom of the Premier League.
Despite a tireless display, it has been a chastening return to the top flight for Scott Parker's side, who have conceded 11 goals – the most they have shipped in the opening four league games since 1960.
Wolves, smarting from their recent loss of form, were tentative but still had too much for Fulham to end a run of three straight defeats.
The Cottagers were sharper than their hosts in the opening 20 minutes, but Wolves slowly began to take control.
Yet, lacking confidence after their run of losses, including a 1-0 Carabao Cup exit to Stoke, the hosts' usual zip was missing.
It did not help that Nuno opted for the conservative pick of Romain Saiss out of position at left-wing back, with Ruben Vinagre close to a move to Olympiacos and a deal for Angers left-back Rayan Ait-Nouri not yet complete.
They needed Tim Ream to gift them a chance after 27 minutes, only to be denied by Areola's brilliance.
Neto intercepted the defender's sloppy pass and his low strike was parried by Areola, who was up quickly to deny Semedo from close range.
It was a rare chance in a combative but forgettable half and Wolves have now failed to score in the first half in 19 of their last 25 top-flight games.
Ruben Neves fired wide soon after the break before Areola came to Fulham's rescue again after 55 minutes.
Max Kilman's hopeful long ball sent Raul Jimenez through and he was thwarted by Areola's legs, with the goalkeeper claiming Leander Dendoncker's follow-up.
The reprieve did not last long as Areola was finally beaten a minute later when Neto grabbed his first goal of the season.
Dendoncker's shot was blocked by Robinson and, as Fulham failed to clear, the ball ricocheted to Neto, who drilled into the bottom corner from 16 yards.
It was a reward for an energetic opening to the half, but the Cottagers should have levelled after Ademola Lookman brilliantly worked the ball to Aleksandar Mitrovic.
The striker unselfishly squared to Kamara, unmarked eight yards out, but he could only tamely sidefoot straight at Patricio.
It summed up Fulham's afternoon and Neeskens Kebano drilled over with a minute left as the Cottagers faced up to another defeat.