Chelsea endured a scare in the company of Wolves but emerged smiling thanks to second-half goals by Pedro and Diego Costa. It was the right result in the end but the Championship team can take pride from how difficult they made life for their illustrious visitors.

Wolves bumbled into this tie on the back of three consecutive defeats but to lift morale Paul Lambert needed only to refer to their previous performances in this competition. Victories away to two Premier League teams – Stoke City and Liverpool – had proved their capacity to antagonise the elite. To stretch a point he might even have recalled that Chelsea only drew at Anfield, a result that meant Antonio Conte’s team had failed to win either of their previous two away matches, although using that evidence to suggest the Premier League leaders were in the midst of a stutter might have pushed the glass half-full approach so far it invited questions as to just which drink the glass was half-full of. But hey, the FA Cup is no place for moderation of ambition.

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Conte made seven changes to the lineup who had started Chelsea’s last match but, make no mistake, he was aiming to preserve his team’s chances of marking his debut season in England with a domestic double. The upsets caused by Lincoln and Millwall earlier in the day led him to reinforce that message to his team. “After those results I tried to warn the players about the difficulty of this game,” he said. This manager does not neglect any competition and, as ever, his manic contortions on the touchline attested to his yearning for victory.

So did the strength of his team in spite of the changes. He retained Costa and Eden Hazard, and the players drafted in were not exactly nobodies, with Cesc Fàbregas beginning in midfield and John Terry leading a defence featuring Kurt Zouma and Nathan Aké.

Roared on by the biggest Molineux crowd since 1981, Wolves tore into their visitors. They came agonisingly close to drawing blood in the fourth minute, when Zouma failed to clear a cross by Conor Coady and the ball broke to George Saville, alone 12 yards from goal. Excitement got the better of the midfielder, a graduate of Chelsea’s academy, and he rather slashed at the ball, which hurtled past Asmir Begovic but bounced back off a post.

Wolves radiated energy but also passed slickly and they continued to worry the visitors. They also defended tightly during the inevitable spells when Chelsea forced them backwards.

Fàbregas undid Wolves’ rearguard with a classy touch in the 12th minute, dissecting the defence with an artful through-ball to Willian. Carl Ikeme charged off his line to parry Willian’s shot and then foiled his rebound, too. Eight minutes later Willian had a let-off in his own box, when the referee ignored febrile appeals for a penalty when Andreas Weimann hit the ground under the weight of a challenge by the Brazilian.

It was an even and exhilarating contest, with a cracking tempo and crunching tackles – wholesome entertainment despite the blank scoresheet at half-time.

The onus was on Chelsea to demonstrate their superiority in the second half but within a minute of the resumption they were thrown into panic at the back by a dash down the right by Hélder Costa. They survived but were patently unnerved and Pedro was booked moments later for resorting to a trip to sabotage another burst by the winger.

Fàbregas and Nathaniel Chalobah formed a less forceful midfield duo than N’Golo Kanté and Nemanja Matic, at times outrun and outfought, but when Chelsea attacked their moves usually flowed through Fàbregas. His pass before the hour led to a chance for Victor Moses, whose shot was deflected wide. In the 62nd minute Willian pinged a low pass to Costa, who twisted past Danny Batth but fired into the side netting. The pressure was building.

The breakthrough came in the 65th minute and there was no disputing its quality. Costa and Hazard conspired deftly before Willian floated in a perfect deep cross. Pedro arrived to head into the net from 10 yards.

Conte replaced Pedro with César Azpilicueta and then introduced Kanté for Willian. He was taking no chances. Wolves were left to regret missing theirs, especially when Costa pounced on a loose ball and swept it into the net in the last minute.

“I’m proud of my team because we made this game what it was,” said Lambert, who was similarly impressed with Chelsea. “It’s going to take one hell of a team to stop them doing the double,” he said.

“It is too early to talk about this,” said Conte of his side’s double prospects, but he was happy to praise his hosts’ display. “Wolverhampton deserve my compliments for the performance because they played very well,” he said. “They showed good organisation, character and intensity.”