It was even first period for both sides, with chances from George Saville, Willian and Costa but all failed to draw the first blood in the Midlands.
Antonio Conte's side took over in the second 45 minutes, with an opportunity for Costa before Pedro opened the scoring in the 65th minute. Chances from Willian followed before Costa secured their passage in the 89th minute.
An even start
Chelsea are cruising in the league, but cup success were also on their minds as they headed to Molineux and Paul Lambert's side certainly gave them a scare from the first whistle.
Wolves had the best opportunity of the half just five minutes in, when Kurt Zouma failed to deal with a long punt forward. It landed at the feet of Saville 12 yards out, and though he caught it well it clattered off the frame of the goal.
The visitors then started to come into the contest after that scare, with their first opportunity of merit coming in the 12th minute. Cesc Fabregas did brilliantly to pick out Willian, with the Brazilian juggling his way into the area but his eventual effort was palmed away by Carl Ikeme.
The Blues also ended the half well, with an excellent chance in extra-time. Victor Moses did well down the right before fizzing a ball into the mixer, he found Costa who was heavily marked but he hooked his effort over the crossbar.
Drawing first blood
The beginning of the second period was a lot more quiet than the first, but Chelsea remained strong as they looked to chip away at their opponents.
Willian did well to find Costa in the 62nd minute as the Spaniard brilliantly held off Danny Batth, he only had the goalkeeper to beat but the tight angle failed him as he could only find the side-netting.
They managed to finally break through in the 65th minute, and managed to take the lead with some class. Costa did well to hold up the play before sending Willian away, he floated a great ball into the back post where Pedro was waiting to head home from close-range.
Seeing it out
Once they had the first sniff the visitors were looking to kill off their opponents, and had some great chances to do so as the clock ticked down. Willian did well to dance past Kortney Hause to get on the end of Fabregas' ball, he looked favourite to beat Ikeme but the keeper did well to come out and block.
With a minute of normal time remaining, Chelsea managed to land the killer blow with their second of game. Fabregas had been a danger throughout and was at it again as he gives it to Costa, and in a blink of a eye he had picked out the far corner to see them into the last eight.