Drogba turned home a ball from John Terry in the 68th minute at Wembley and Malouda side-footed home a right-wing cross from Michael Ballack in the 89th. Lampard stroked home the third in injury time after a Chelsea breakaway.
In the May 15 final, Chelsea will face the winner of Sunday's semifinal between Tottenham and Portsmouth.
The final scoreline was hard on Villa, which controlled much of the game but caved in during the final stages.
Although Chelsea beat Villa 7-1 in a Premier League meeting two weeks ago, Carlo Ancelotti's team failed to recapture that form. Currently leading the Premier League, however, Chelsea is still on course to complete the league and cup double.
A minute after James Milner's low shot from just outside the area flashed past the Chelsea post, Villa should have had a penalty in the 16th.
John Obi Mikel challenged Gabriel Agbonlahor who went down as he spun toward goal but referee Howard Webb waved away Villa's penalty appeals to leave manager Martin O'Neill raging at the officials.
The notorious Wembley pitch, which has been re-laid several times since the stadium was rebuilt, caused frequent problems with players slipping and forced to change their boots.
Villa defender Stephen Warnock blocked a 12-meter (yard) shot from Drogba and Joe Cole forced a near post save from Brad Friedel as Chelsea threatened. But it was a poor quality game full of misplaced passes as Chelsea struggled to break down a well-organized Villa defense.
John Carew went close to giving Villa the lead from Stewart Downing's corner early in the second half but his glancing header flew past the far post.
Chelsea sent on Salomon Kalou but went ahead thanks to a piece of good fortune.
Malouda's badly directed corner was poorly cleared to Terry, whose left-foot drive appeared to be going wide but was turned in by Drogba from six meters (yards).
Villa sent on striker Emile Heskey late in the game but it was 2-0 in the 89th when Malouda arrived at the far post to turn home Ballack's well flighted cross.
Lampard's third came in the third minute of injury time after Chelsea had cleared a Villa move and the midfielder, who scored four goals in the 7-1 league victory, was left unmarked to shoot home from 12 meters (yards).
