There were fears Finch's series might be over after he received a nasty blow on his right glove from a searing short ball from Mohammed Shami on the stroke of tea on day three.
Finch, who retired hurt on 25, went to hospital for X-Rays amid concern that he had suffered a fracture to his right index finger.
Scans confirmed there was no fracture and he batted in the Perth Stadium nets before play resumed on the fourth day.
Australia, 1-0 down in the four-match series, were 132 for four in their second innings overnight with a lead of 175 runs.
(Reporting by Tristan Lavalette; editing by Nick Mulvenney)
