After Fikayo Tomori had netted his first goal for the Blues with a stunning 25-yard strike, Abraham netted three times in the space of 21 minutes to take his tally to seven from his last three outings.
The England international put through his own net before Patrick Cutrone scrambled home from close range to give Wolves hope heading into the final minutes.
However, Mason Mount capped another fine display with a well-taken individual goal to help move Chelsea into sixth position in the standings, while Wolves drop into the relegation zone after extending their winless run in the top flight to five matches.
Having witnessed his side record just one win from five games before the international break, Frank Lampard went with three at the back for this contest in order to match up with Wolves' tried-and-trusted strategy.
While the visitors dominated possession during the opening stages, neither side created anything of note at either end, resulting in somewhat of a stand-off.
The Blues had been building momentum as the game approached the half-hour mark, but few could have predicted the manner in which they would take the lead in the West Midlands.
After the ball fell invitingly for him around 25 yards from goal, Tomori deceived Rui Patricio with a curler from distance, eventually finding the far top corner after the goalkeeper had initially moved in the opposite direction.
Chelsea required just three more minutes to double their advantage. Tomori linked up with Mount, who was pulled down by Conor Coady as he attempted to find Abraham, but the ball was collected by the striker who fired past Patricio on the turn from 10 yards out.
Wolves had been left shell-shocked as they still awaited their first effort on goal, and Chelsea heaped more misery on their hosts before the break with Abraham sending a bullet header into the corner after meeting Marcos Alonso's cross from the left.
Raul Jimenez wasted a header of his own just before the half-time whistle, although conceding during the opening 45 minutes would have been harsh on Chelsea after their most complete 45 minutes under Lampard's guidance.
However, while the home side inevitably had more joy in the final third, it was not long before Abraham completed his hat-trick in impressive fashion, shaking off the attention of Coady before firing low in the far corner from eight yards.
The Blues should have netted a fifth as the game entered the final quarter after Mount rounded Patricio, but the newly-capped England international could only find the side-netting with his shot.
Given their dominant position, Lampard would have been eager to see his side keep their first clean sheet of the campaign, especially ahead of encounters with Valencia and Liverpool over the next eight days.
While the game felt over as a contest, Wolves continued to try to salvage some pride, and they further reduced the deficit with six minutes remaining as Cutrone bundled the ball into the net from inside the six-yard box.
Witnessing their side further reduce the deficit naturally led to the home supporters cranking up the decibel level inside Molineux, although it equally resulted in any complacency disappearing from within the Chelsea ranks.
Substitute Michy Batshuayi squandered two opportunities either side of six minutes of added-on time being signalled, but Mount confirmed the three points in style by cutting inside onto his right foot before finding the far bottom corner of Patricio's net.
WOLVERHAMPTON WANDERERS (3-5-2) Patricio; Vallejo, Coady, Saiss; Traore (Doherty 56'), Dendoncker (Cutrone 46'), Moutinho, Neves, Jonny; Jota, Jimenez (Gibbs-White 70')
CHELSEA (3-4-2-1) Arrizabalaga; Rudiger (Zouma 46'), Christensen, Tomori; Azpilicueta, Jorginho, Kovacic (Barkley 70'), Alonso; Willian, Mount; Abraham (Batshuayi 77')