The Greece striker fired high past Jonny Tuffey in the 33rd minute to give the holders the interval lead.
In the 67th minute, after Caley defender David Proctor had conceded a penalty for a foul on Gary Hooper, Parkhead skipper Brown slotted in the spot-kick for his third goal in three games to take the holders into Monday's draw at Hampden.
Source: PA
Source: PA