Michu scored his 16th goal of the season, and Danny Graham added a late second to put the Swans within touching distance of their first ever major Wembley cup final.
Laudrup admitted the performance was one of the best since he took charge in the summer, but warned his side could ill afford to begin thinking about a Wembley final.
“I’m delighted with the result. I would lie otherwise,” he said.
“I think we have had some historic results already this season — winning at Anfield and at the Emirates. Winning at the European champions though is something very special.
“But there is still a mountain to climb. They have so much quality and we will have to play exactly the same; with the same intensity.
“They could still score three of four goals against us. But I am most happy about going into the second leg at home with a possibility to play a final at Wembley.”
In truth, Swansea did not have to work hard for their victory. With the exception of David Luiz, Chelsea were very poor throughout. Sloppy in possession and lacking a cutting edge in attack, the Blues looked anything like title challengers or potential cup finalists.
Fernando Torres was the worst offender. The former Liverpool striker has shown signs of improvement since Benitez’s appointment, but last night the Spaniard’s two chances amounted to a weak header and a long-range shot that almost found the second tier of the Shed End. He touched the ball 19 times during his 81 minutes on the pitch.
“We had a lot of chances and could have scored two or three in the first half, one or two in the second,” said Rafa Benitez. “We made two mistakes and paid for them... if we played this game 10 times maybe we would win nine of them.”
Chelsea’s fans spent a large chunk of the match berating Benitez for his failure to bring on Demba Ba, who scored twice on debut last weekend, and they also took umbrage with the interim boss’s failure to bring on Frank Lampard until the 70th minute.
Blues fans have not hidden their dislike towards Benitez since his appointment, but last night they gave him both barrels, booing the Spaniard’s decisions and calling for the return of Roberto Di Matteo in the dying minutes of the defeat.
Torres’ only decent contribution of the opening 45 minutes came when he split the Swansea defence, but Tremmel came to the Swans’ rescue.
A quiet hush fell upon Stamford Bridge, with the hosts’ lack of penetration up front clearly dampening their enthusiasm.
The most noise the home support displayed was when Lampard emerged from the dugout to warm up.
The Blues fans fell silent moments later, however, when Ivanovic’s error gifted Swansea the lead. Jonathan de Guzman pinched the ball off the Serb as he dallied on the edge of his own box and squared to Michu, who calmly slotted the ball past Ross Turnbull.
Luiz, Chelsea’s best player, went close with two efforts after the break.
The home fans started to vent their anger at Benitez for not introducing Ba or Lampard. One fan had to be restrained by stewards as he headed in the direction of the Chelsea bench. Another invaded the pitch. The rest of the crowd continued to demand Lampard’s introduction. Benitez eventually beckoned the midfielder over to tell him he wanted him to come on with 20 minutes to go.
Lampard injected life in to the Chelsea, but Torres continued to perform poorly.
Benitez finally answered the home fans’ demands and brought on Ba with nine minutes left. Torres departed to cheers and a sarcastic standing ovation.
Ba made an immediate impact, going close with two efforts, the second a looping header from Marko Marin’s cross.
Ba hurtled through injury time and went down after Tremmel failed to collect the ball, but the referee did not give a penalty and instead booked the former Newcastle man for diving.
Chelsea’s night then turned worse with one minute of added time left. Ivanovic’s second terrible backpass allowed Graham to pinch the ball off Turnbull before slotting into the net.
Ba thought he had pulled one back for the Blues moments later but his effort was ruled out for offside. “The goal was level, and so a goal,” said Benitez. “The penalty, the yellow card, we can talk about. It was not a yellow card but the penalty depends on the vision of the referee. Swansea have a great advantage but we have to go there, try and score and we will be in the game.”
CHELSEA: Turnbull, Azpilicueta, Ivanovic, Cahill, Cole, Luiz, Ramires (Lampard 71), Hazard, Oscar (Marin 83), Mata, Torres (Ba 81).
SWANSEA: Tremmel, Rangel, Chico, Williams, Davies, Britton, de Guzman, Ki, Routledge (Tiendalli 62), Hernandez, Michu (Graham 83).
Referee: Anthony Taylor.