A last-minute equaliser from young Steven Naismith earned Kilmarnock a replay that they scarcely deserved. For long periods Hearts were camped in Kilmarnock's box, and it took an outstanding display of goalkeeping from Alan Combe to keep Killie in the cup.
But it was a fantastic way for Naismith to end a memorable week.
He has just signed a new contract for the club, and his goal in the dying secoinds was his first for Kilmarnock's top team.
Hearts will be furious at having to go back to Rugby Park for a replay as they had enough chances to win the game comfortably.
To be fair, they weren't guilty of squandering chances as much as being victims of an outstanding goalkeeping display by Combe.
Hearts took the lead after 15 minutes when Robbie Neilson's cross form the right found Dennis Wyness in acres of space to guide home a header.
And Combe made smart saves to deny Paul Hartley and Stephen Simmons before Kilmarnock got an equaliser.
Allan Johnston's cross from the right wing bobbled about Hearts' box, and Colin Nish reacted quickest to nod the ball home.
Hearts had the Kilmarnock defence in all sorts of trouble, and Combe continually bailed them out until seconds before half-time when Hearts crafted an excellent second goal.
Hartley was the architect with a superb 60-yard burst, and he then teed up Lee Miller to smash home an 18-yard drive.
Kilmarnock went all out for an equaliser after the break but struggled to penetrate Hearts' defence, despite plenty of corner kicks.
That was until the last minute when young Naismith latched on to Kris Boyd 's knockdown to hammer a haf-volley into the top corner.