Dicko had been on-loan at Molineux from Wigan last season and joined the club on a permanent basis for £300,000 earlier this month.
He gave promotion-chasing Wolves a 10th-minute lead and then saw his cross deflected into his own net by Derrick Williams after Sam Baldock had equalised for the visitors from the penalty spot.
Substitute Bakary Sako then made the game safe with a clinical finish in 76th minute.
Dicko broke the deadlock when he beat goalkeeper Elliott Parish at his near post with a powerful drive after being picked out by Jack Price.
His good work looked to have been wasted 14 minutes later when Greg Cunningham was pulled down in the area by James Henry and Baldock sent Wolves keeper Aaron McCarey the wrong way from the spot for his 15th goal of the season and his sixth in as many league games.
But the lively Dicko was not to be denied and his right-wing cross in the 44th minute flew into the net off Williams.
Sako then rifled home a fierce shot from the edge of the area to snuff out relegation-threatened City's comeback hopes as their five-game unbeaten run came to end and their winless run at Molineux was extended to 21 matches, stretching back to 1931.