The Premier League leaders took over an hour to break down the Championship strugglers and Blues boss Antonio Conte was an animated figure on the Molineux touchline as his side laboured for long periods against a team they were comfortably expected to beat.
However, Pedro connected with Willian's cross to head home his fourth FA Cup goal of the season and maintain his record of having scored in every round of the competition, before Diego Costa rounded off the win in the closing stages.
It may have been a different story had Chelsea youth player George Saville found the net with a shot that rattled the frame of the goal in the 10th minute for Wolves, but Paul Lambert's men offered little goal threat thereafter and slowly the visitors began to show their quality.
Wolves had dumped Stoke City and Liverpool out in their previous two rounds, but Chelsea proved a step too far and the home side were lacking in all departments leaving Lambert to turn his focus to steering Wolves - who are 19th - away from the relegation zone.
Wolves made a bright start and Conor Coady's looping cross forced Asmir Begovic to punch the ball over the crossbar, before an error by Kurt Zouma afforded former Saville a golden opportunity to score but his shot crashed onto the post and bounced clear.
Cesc Fabregas, making his 100th Chelsea start in one of seven changes from the 1-1 draw with Burnley last time out, beautifully weighted a pass to put Willian clean through on goal for Chelsea but the Brazilian failed to get a shot away, and Chelsea struggled to retain possession as Wolves tirelessly harried and pressed them.
Wolves were given ample time and space in Chelsea's half of the field and Helder Costa turned neatly before firing a shot into the arms of Begovic, but there was a sense that the visitors were only biding their time before stepping up a gear.
The more involved Eden Hazard became, the more Chelsea threatened but the skilful Belgian too often cut a lonely figure on his mazy dribbles and Wolves were able to shackle him with some robust challenges.
Both Pedro and Zouma wastefully shot wide from distance as Chelsea started to open Wolves up with some neat passing, and Costa hit the side netting with his first clear chance of the game after turning Danny Bath inside the box.
The breakthrough arrived in the 65th, though. Fabregas and Costa split the Wolves defence before Willian sent over a cross that left the unmarked Pedro with a straightforward header at the back post.
Chelsea might have doubled their lead when Fabregas put Willian through, but Kortney Hause did just enough to block his shot.
But the visitors did have a second when substitute N'Golo Kante's run and pass provided Costa with an opportunity that he finished with aplomb, shooting low into the corner of the net.