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.
With the exception of David Luiz, Chelsea were very poor throughout with Fernando Torres the worst offender as his two chances amounted to a weak header and a long-range shot that almost found the second tier of the Shed End.
Torres started lively enough, drifting out to the left flank where he delivered a clever cross to the front post, but Branislav Ivanovic headed over. The Spaniard then picked the ball up 30 yards out and crept towards goal before firing a wayward shot that cleared the bar by many metres.
Chelsea thought they should have had a penalty when Ki Sung-Yueng grappled with Luiz while going for cross but Anthony Taylor waved play on. Efforts from Cesar Azpilicueta and Gary Cahill both went wide while Juan Mata lost his usually clinical touch in front of goal after a foray in to the box by Eden Hazard.
Another brilliant move came on the half-hour with Oscar backheeling the ball in to Mata from Ramires' pass, but once again the former Valencia man shot wide. Torres' only decent contribution of the opening 45 minutes came when he split the Swansea defence, but Gerhard Tremmel came to the Swans' rescue.
Ivanovic's error then 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. Frank Lampard was brought on with 20 minutes to go and the England man injected some degree of life.
Ki then sent Michu through with a clever pass, but the linesman flagged for offside just as the former Rayo Vallecano man was about to pull the trigger. Benitez finally answered the home fans' demands and brought on Demba Ba with nine minutes left.
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 in to an empty net. Ba thought he had pulled one back for the Blues moments later but his effort was ruled out for offside.