Myler kicked six from six penalties and a conversion in his 20-point-haul as Northampton, dominant at the scrum and breakdown, applied relentless pressure after the break.
George Ford was successful with three penalties and a conversion for Bath who had crossed for the opening try when winger Anthony Watson touched down.
Northampton will look to secure a trophy double at the end of the month when they face Heineken Cup finalists Saracens in the English Premiership final.
(Reporting by Justin Palmer; Writing by Ken Ferris)
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