Mark Roberts' second-half penalty proved decisive as Ayr overcame Falkirk 2-1 in the fifth round of the Scottish Cup.
Visitors Falkirk were first out of the blocks against their First Division rivals and took an early lead through Blair Alston.
Thomas Scobbie found space to cross from the left and Alston was on hand to head home beyond Ayr goalkeeper Kevin Cuthbert.
However, Brian Reid's side were level with 19 minutes gone as Andrew Geggan nodded into the bottom corner from close range after Adam Dod clipped a dangerous cross into the Ayr box.
The tie remained in the balance until shortly before the hour when Darren Dods handballed inside the Bairns' area.
Roberts stepped up confidently to dispatch his spot kick low past Cuthbert and book a home clash against Hibernian in round six.
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