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He will now meet world No 159 Blaz Rola in Friday s quarter-finals, and will be looking to improve in some areas after managing to take advantage of just three of the 12 break points he created.
Three-time Grand Slam champion Murray appeared to be cruising after a double-break opened up a 5-2 lead on the Palapajetta Court.
But the Italian fought back by winning the following two games to make the Scot more nervous.
However, Murray stayed calm under pressure and managed to serve the set out at the second time of asking in just under an hour.
Murray beat German world No 203 Maximilian Marterer 6-7 6-2 6-3 on Tuesday too