The lead was doubled shortly before the break, as Harley was quickest to a loose ball in Bristol's box to score.
John Akinde pulled a goal back for the Robins on 63 minutes, but Nardiello restored the two-goal margin within a minute to secure the win for Exeter.
The friendly was the first time a game had been played on the newly laid pitch at St James Park.
Source: BBC Sport
Source: BBC Sport