Largs suffered a 2-1 reversal at the hands of their Ayrshire rivals in Saturday's McBookie.com West 1st Division league clash.
Eddie McTernan popped up with the winning goal after a goalmouth scramble with six minutes to go.
It was tough on Largs who had been on the ascendancy in the first half but failed to convert their chances but Begley converted from a corner with a header on the stroke of half-time.
A John Carter equaliser for the visitors on 55 minutes was followed by a straight red card for Thistle forward Jamie Campbell.
Largs boss Stuart Davidson said: " I am still quite gutted at the result as I thought it was a decent display, specially in the first half where at a point we could have scored two or three goals. But at the end of the day, it is critical that you take your chances, and while I thought we defended well against Irvine Meadow from open play, we didn't do well enough from their set plays and corner kicks."
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