The best chance of the first half fell the way of the hosts, as midfielder George Saville sent a shot against the post when picked out unmarked inside the box.
Premier League leaders Chelsea plugged away in the second period and were rewarded when Pedro headed home on the hour, before Costa added a second late on by picking out the bottom corner to seal the win.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Begovic; Zouma, Terry, Ake; Moses, Chalobah, Fabregas, Pedro; Willian, Costa, Hazard
SUBS: Eduardo, Azpilicueta, Cahill, Kenedy, Kante, Loftus-Cheek, Batshuayi
STARTING XI: Ikeme, Coady, Batth, Hause, Doherty, Price, Saville, Costa, Edwards, Weimann, Bodvarsson
SUBS: Burgoyne, Stearman, Evans, Saiss, Ronan, Gibbs-White, Enobakhare
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Paul Lambert: "On any given day we can win. But we have to perform. As long as we play the game and not the occasion we'll see what happens. We've got to stay in the game. In the FA Cup we've won the club's first game in six years, which is incredible, then the Liverpool game was iconic which will live in a lot of people's memories. Now there's another chance of something special. I'm delighted for the supporters because these are the games you want to be involved in. They don't happen every week, so when you do get one you make sure you have no regrets as a supporter as a player."
Antonio Conte: "Usually I like to win and I like to try to win with my team, every competition in every season. We must have this winning mentality. When you are Chelsea's coach or you are a Chelsea player, you must have this ambition to try to win every competition that you play. For sure it won't be easy. In the league there are six teams very strong to fight until the end to win the title. In the FA Cup there are 16 teams. Our target now is to go into the next round. This game won't be easy. Don't forget Wolverhampton won against Liverpool away, won against Stoke away."
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WOLVES SUBS: Burgoyne, Stearman, Evans, Saiss, Ronan, Gibbs-White, Enobakhare
CHELSEA SUBS: Eduardo, Azpilicueta, Cahill, Kenedy, Kante, Loftus-Cheek, Batshuayi