The touchdowns enabled the former England centre, capped twice on the 2009 summer tour to Argentina, to open his account for Northampton after arriving from French side Toulon during the close season.
Russian winger Vasily Artemyev added two more to take his tally to six in three matches since arriving at Northampton following the World Cup, with England winger Chris Ashton scoring the fifth and sixth.
Ryan Lamb, who was involved in the build-up to the first three tries, contributed 12 points, with two penalties and three conversions, with his replacement Stephen Myler adding a conversion.
Kiwi fly-half Jimmy Gopperth scored all Newcastle's points, with four penalties and a drop goal.
Lamb and Gopperth exchanged penalties in the first five minutes before May put Northampton ahead against the club where he spent 10 years before leaving for France in the summer of 2009.
Samoa prop Soane Tonga'uiha charged down Newcastle scrum-half Chris Pilgrim's clearance kick and the Saints moved the ball left before Lamb released a well-timed pass to send May over after 12 minutes.
Eight minutes later May struck again following a powerful drive by Tonga'uiha.
Newcastle were having real problems holding the powerful prop and this created space for Lamb to feed the short pass which sent May in near the posts, leaving Lamb, who had missed his first conversion attempt, an easy kick.
But Gopperth kept the visitors in contention with two penalties.
The second came after England lock Courtney Lawes was yellow-carded for a blatant late challenge which felled Jeremy Manning after the Newcastle full-back had kicked the ball downfield.
Gopperth reduced the deficit to three points with a well-struck drop goal in the 37th minute but Lamb landed his second penalty on the stroke of half-time, after the Newcastle scrum was penalised, to send Saints in with an 18-12 interval lead.
Northampton and Newcastle started the match in 11th and 12th positions respectively but the Saints, relishing the return of their international contingent from the World Cup, pressed on to seal their fourth successive victory - two in the Premiership and two in the LV= Cup.
Tonga'uiha and England hooker Dylan Hartley have strengthened the front row with Lawes and flanker Tom Wood making their presence felt behind them, while the back three of England full-back Ben Foden, Ashton and Artemyev have greatly added to their attacking options.
Newcastle kept a close watch on the Russian, already scorer of four tries in his opening two matches for Northampton.
But Artemyev struck in the 44th minute as Newcastle paid the penalty for losing a lineout when hooker Joe Graham overthrew the ball.
Northampton number eight Phil Dowson - another former Falcon - capitalised with a powerful run before Lamb and centre Jon Clarke combined to put the Russian in.
Artemyev secured the bonus point with his second 10 minutes later, as May and Clarke linked to create the overlap.
Ashton got in on the act, complete with trademark swallow dive, following another fine line break by Dowson who sent him in between the posts, with Lamb landing his third conversion.
Ashton struck again five minutes from time when he snapped up a loose ball inside his own half and raced 60 metres to dive over before Myler converted.
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