The Southend keeper also saved brilliantly from Ashley Cole's 12-yard shot during another first-half assault by the Blues.
Chelsea pushed hard for a second goal after the break, with Mildenhall called into action again to stop Drogba's effort, before the keeper was was forced to punch clear off the head of Ricardo Carvalho.
He could do nothing to prevent Belletti's header creeping into the net, but fortunately for the shot-stopper, his team-mates and the travelling fans, Herd was on hand to clear off the line.
That interception proved crucial to Southend, 13th in League One, when Clarke nodded in at the far post to set up a Roots Hall replay on Wednesday 14 January.
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