Holders Chelsea reach FA Cup final
All three goals came late with Didier Drogba breaking Villa's resistance after 67 minutes before Florent Malouda (89th) and Frank Lampard, deep in stoppage time, gave Chelsea an ultimately comfortable but flattering margin of victory.
Defeat left a sour taste in the mouth of Villa manager Martin O'Neill who said referee Howard Webb should have given his side a clear first-half penalty.
O'Neill added that Chelsea skipper John Terry should have been sent off for an "horrendous" second half tackle on his England team-mate and Villa midfielder James Milner.
"It's a straightforward red card," the Villa manager said. "James is exceptionally lucky to have his career intact. James is very sore and he's very lucky. It was a pointless challenge but it was made and Terry should have had a red card."
He was also angry that Webb denied Villa a penalty when Jon Obi Mikel brought down Gabriel Agbonlahor right in front of him.
"I thought it was an injustice. You expect quality referees to get straightforward decisions correct," he said.
Chelsea manager Carlo Ancelotti admitted Chelsea had to improve after a poor first half.
"We were lucky to stay in the first half at 0-0. The second half was really a different story," he said.
The Italian also praised Drogba who took his tally for the season to 32 goals.
"He's working very hard for the team," said Ancelotti. "It doesn't matter if he starts the game or not, it's important that he scores the goals."
He did just that to break the deadlock and has now netted in all five cup matches he has played for Chelsea at Wembley Stadium.
The opening goal came when he turned a Terry shot into the net past goalkeeper Brad Friedel.
Malouda added the second after a cross from substitute Michael Ballack and Lampard grabbed the third just before the four minutes of added time ended.
Chelsea, with a place in the final for the 10th time, now meet Tottenham Hotspur or Portsmouth, who play in the second semi-final on Sunday, in the showpiece at Wembley on May 15.
The final scoreline belies the close nature of the match, as Villa, determined to atone for a 7-1 Premier League loss at Chelsea two weeks ago, matched the favourites stride for stride.
At least they did when the players were not falling over on a slippery pitch which made flowing football hard to achieve.
Although Villa had their chances and went close to taking the lead when John Carew glanced a header just wide early in the second half, Chelsea were the better team overall.
Villa restricted the holders to just two half-chances in the opening 30 minutes as they sought their first appearance in the final since they were beaten by Chelsea in 2000.
They were also fired up after losing to Manchester United in the League Cup final at Wembley six weeks ago, and stretched Chelsea down both flanks where Ashley Young and Stewart Downing supplied pace and crosses.
Drogba, who had scored for Chelsea at Wembley in the 2007 FA Cup final, the 2008 League Cup final, and the 2009 FA Cup semi-final and final, almost struck again after 66 minutes but was unable convert a loose ball after a surging run.
However, he did score a minute later when Villa failed to clear and paved the way for another FA Cup final appearance.