Leicester gave an early taste that they had not arrived as sacrificial lambs when their captain McAuley rose unchallenged to head home a free-kick.
Before Wednesday Lampard had not scored since August, but the England midfielder got back in the goalscoring groove when he finished off a three-man move to equalise.
Scott Sinclair played a key role in that goal and the youngster set up Chelsea's second when his cross bobbled loose to Lampard, who volleyed home.
Fulop made three crucial saves, twice denying Claudio Pizarro and pushing an effort from Sinclair on to the post.
But the home side lost Paulo Ferreira just after half-time. The right-back was stretchered off with an injury to his right ankle.
Campbell punished Chelsea's profligacy in the 69th minute when he headed Levi Porter's chip over the advancing Cudicini and into the net.
Five minutes later Alan Sheehan's free-kick was missed by everyone except Cort at the far post and the former Wimbledon striker swept the ball home.
But Shevchenko levelled for Chelsea in the 87th minute and in the dying seconds Lampard's header squeezed over the line to provide a dramatic winner.
