Frank Lampard, captain in the absence of injured John Terry, scored the other two in the second half.
Shevchenko, whose poor form since his 29 million pound transfer from AC Milan last May has prompted a raft of headlines in recent weeks about tension in the Chelsea camp, looked lively from the start of the second-leg game.
After flicking a chance wide in the second minute and having a shot blocked in the 14th, Shevchenko picked up a poorly directed pass from midfielder Tommy Doherty, 30 metres out. He ran at advancing Wycombe keeper Ricardo Baptista and flicked the ball low into the bottom corner of the net in the 22nd minute.
It was Shevchenko's first goal since December 5 and prompted coach Jose Mourinho to leap from the home dugout with his fists pumping in celebration.
STRONG SIDE
Mourinho had fielded a strong side against the lowly club who forced a 1-1 draw in the home leg two weeks ago, playing Shevchenko from the start rather than using him as substitute has he has done in recent weeks.
Two minutes before halftime, Shevchenko justified that opportunity again when strike partner Didier Drogba chipped the ball forward and, with Wycombe defenders wrong-footed and clamouring for offside, the Ukrainian lifted it deftly over Baptista.
The London side, who won the League Cup two years ago to earn Mourinho his first English trophy, took control in the second half and it was only Ricardo Baptista's keeping and sloppy finishing from the home side that kept the scoreline in check.
Chelsea put the tie beyond doubt in the 68th minute when England midfielder Lampard capitalised on some scrappy defending, rounding Wycombe's back line and Baptista, who had run out of his area, to coolly slot home.
Wycombe, who put Premier League sides Fulham and Charlton out of the competition in earlier rounds, tried to push forward but they left yawning gaps at the back. In the 90th minute Lampard took full advantage running down the middle to receive a pinpoint pass from Drogba and notch his second.
Mourinho substituted Shevchenko late in the game, greeting him with a thumbs up and handshake in stark contrast to recent matches where their contact appeared decidedly frosty.
Chelsea will meet Arsenal or Tottenham Hotspur in an all-London final at Cardiff's Millennium Stadium on February 25.
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