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Freddie Burns kicked the visitors to an early lead, but Pisi pounced twice before the half-hour mark to open up a lead for the Saints.
Both sides defended hard for much of the second half, as only Lee Dickson was able to add to the score in the first 30 minutes after the restart, extending the hosts' lead by three points.
The visitors tired towards the end, though, allowing Alex Day for two tries in the last eight minutes of the match.
The result ensures that Northampton begin their Anglo-Welsh Cup campaign with a bonus-point win.