Leicester were soon into their stride and had claims for a penalty turned down after a challenge by Marcel Desailly on Muzzy Izzet.
They then went ahead after 24 minutes when Stefan Oakes sent over an outswinging corner and Scowcroft timed his jump perfectly to send a downward header past the dive of Carlo Cudicini.
Chelsea got back on level terms in the 62nd minute with Hasselbaink's 21st goal of the season.
Graeme Le Saux sent over a left-wing cross which was flicked on by Forssell - and Hasselbaink did the rest with a close-range header.
Scowcroft put Leicester back in front when he headed in a corner from Oakes.
But Gianfranco Zola marked his 250th appearance for Chelsea by curling home a free-kick for the equaliser with 12 minutes left and then Hasselbaink secured all three points for the Blues in the last minute.
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