The home supporters greeted the half-time whistle with boos but Chelsea were unable to produce a fightback of their own, instead falling two goals behind when the electric Neto beat Silva for pace and picked out Cunha for his second.
The Brazilian then completed his hat-trick from the penalty spot after being brought down by Malo Gusto, sending Petrovic the wrong way with eight minutes remaining to put the result beyond doubt before Silva headed in a late consolation.
Wolves' thoroughly deserved victory moved Gary O'Neil's side up to 10th, one point and one place above Chelsea after 23 games.
O'Neil's Wolves on the rise
With the added incentive that victory at Stamford Bridge would lift them above Chelsea, Wolves brushed off the disappointment of losing out to a 97th-minute winner in their seven-goal midweek thriller against Manchester United to reach the top half of the table for the first time under O'Neil.
Wolves had not completed a league double over Chelsea since 1974-75, nor had they managed to win at Stamford Bridge in any competition since 1979.
That they brought an end to both of those waits on Sunday, in the manner they did, was the latest evidence of the terrific job O'Neil continues to do in his first season in charge.
There was no shortage of standout performers for the visitors, for whom Neto once again starred and went close to a goal of his own when he forced his way into the penalty area but could not beat Petrovic early in the second half.
Meanwhile, in the absence of top scorer Hwang Hee-chan, Cunha has now been directly involved in 12 goals in Wolves' last 12 Premier League games - scoring seven.
After Cunha's strike O'Neil, only appointed on the eve of the new season, immediately switched his attention to issuing instructions and refocusing his team as they extended their advantage in a second half.
But he could not hide his delight as he celebrated at full-time with the travelling Wolves fans, who chanted his name throughout a significant win which leaves their sights fixed on the clubs above them.
More to follow.