Goals from Frank Lampard and Terry gave Chelsea a place in the last four where they will meet Aston Villa at Wembley.
Lampard's opener came in the 35th minute when he fired a rising 20-yard shot into the net and Terry sealed victory 22 minutes from time with a firm header.
Terry was booed and abused all afternoon by Stoke fans who lambasted the defender for his alleged affair with Vanessa Perroncel, the former girlfriend of one-time Chelsea team-mate Wayne Bridge. Terry, stripped of the England captaincy by Fabio Capello because of the lurid headlines concerning his private life, celebrated his second half goal by running to the corner flag and pointing at his captain's armband.
When asked about the abuse, Wilkins replied: "It's happening and John's just getting on with the situation. I'm not too happy about it, but there's nothing I can do. He's dealing with the situation in the only way he can – committing himself to the cause. That was a superb performance from him."He's an exceptional captain and we're delighted to have him on board. He leads these players on the pitch in fantastic fashion and scored a great second goal.
"Terry paid tribute to the club for their support during a difficult period.
"The armband means a lot, of course," said Terry. "Chelsea have been very supportive, the players as well, but we wanted to show the fans how much it meant to us.
"We had a couple of days to work on their set plays but they can play as well. On a dodgy pitch I thought we played well and bounced back from last week," added Terry, in reference to the 4-2 defeat by Manchester City which opened up the Premiership title race once again.
Chelsea certainly did not have it all their own way, and in the 14th minute it required a clearance off the line from John Obi Mikel to prevent Stoke going ahead. Delap's long throw was punched clear by Hilario but only to Dean Whitehead on the edge of the penalty area. The Stoke midfielder's drilled shot was heading for the bottom corner until Mikel's timely intervention.
Chelsea squandered a great chance in the 29th minute when Whitehead was caught in possession inside the penalty area but Nicolas Anelka fired beyond the far post from six yards.
However, Chelsea won a succession of corners and one of them paid off in the 35th minute when Lampard fired them in front with the 18th FA Cup goal of his Stamford Bridge career. Florent Malouda's corner found Terry at the far post and the Chelsea captain laid the ball into the path of Lampard for the England midfielder to send a well-hit drive into the net for his 16th of the season. It was also his 146th career goal for the club and pushed him closer to Peter Osgood's tally of 150.
After Terry had made the game all but safe after 68 minutes, heading home another Malouda corner, Lampard almost grabbed a second in the 75th minute but his dipping 20-yard effort was well saved by Sorensen.
Wilkins said: "Stoke put you under a lot of pressure from dead balls and long throws but our concentration was fantastic." Of Chelsea's semi-final chances, he said: "Aston Villa are a very strong side and beat us earlier in the season. It will be another tough game in the semi-final."
England midfielder Joe Cole was again left out of the starting line-up by Chelsea coach Carlo Ancelotti, but Wilkins insists the player will get his chance."We have a superb squad of players and Carlo has a very difficult task in picking a side," he added. "Everyone merits a place in our team, but that was the side today. Joe's had a very traumatic time with his knee, and you get highs and lows. He'll play plenty of games for Chelsea."
Stoke manager Tony Pulis defended his supporters over their treatment of Terry and claimed that the Chelsea captain will come home a hero if England win the World Cup in South Africa this summer.
"Our fans are brilliant, different class," said Pulis. "John will have to accept he'll take stick. He took stick from England supporters the other night. If John does well in the World Cup and wins it, he'll come back a hero."
Pulis was sorry to see his side's cup run come to an end, but said: "We've knocked Arsenal and Man City out. To pull Chelsea out of the hat at Stamford Bridge was a difficult tie. The players were first class, we gave everything and had a right go