Man of the match Stuart Broad took 2-21 to help limit Sri Lanka, which won the toss, to 128-6 despite a top score of 58 by Angelo Mathews.
Openers Craig Kieswetter (39) and Michael Lumb (33) got the pursuit off to a flying start and allowed England to ease home, Kevin Pietersen (42 not out off 26 balls) sealing victory with four overs remaining. Thissara Perera claimed 2-19 but Sri Lanka was soundly beaten.
England will play either Australia or Pakistan in Sunday's final.
The catalyst for England's victory was its bowlers, who were disciplined throughout and gave their side a great start.
Sri Lanka slipped to 26-3 inside the fifth over, with the seam bowling of Broad, Ryan Sidebottom and Tim Bresnan doing the trick.
Left-armer Sidebottom gave England a fine start by removing the out-of-form Sanath Jayasuriya (1), who edged a catch to England skipper Paul Collingwood at second slip.
Bresnan added the wicket of Tillakaratne Dilshan (9) and Broad picked up the key scalp of Mahela Jayawardene (10) to leave the Sri Lankans reeling. Dilshan miscued a pull to deep square leg while Jayawardene edged to wicket-keeper Kieswetter.
Offspinner Graeme Swann (1-20) removed captain Kumar Sangakkara (16) to further set the innings back at 47-4 off nine overs, although Mathews dominated the late overs to reach his first international Twenty20 half-century, off 40 deliveries.
Kieswetter and Lumb powered England's victory charge with a first-wicket stand of 68 off 49 balls.
They had a few slices of luck, Kieswetter surviving a very close lbw shout and Lumb a couple of run-out scares before blossoming.
Kieswetter struck five fours and two sixes before he was bowled by a slower ball from Lasith Malinga. Lumb hit three fours and two sixes before falling to Perera.
Pietersen, recently returned from England where he was present at the birth of his first child, clinched the win with a six and four off successive balls from Malinga.
