It was the right decision as openside flanker Josh Kaifa celebrated his debut with a try. Falcon was again on target with the conversion and the Magpies led 14-0.
The Stags opened their account in the 23rd minute when winger Isaac Te Tamaki scored. First five-eighth James Wilson converted.
Wilson narrowed the gap with a 30th-minute penalty.
Dixon extended the Magpies lead with a 39th minute try. Falcon added the conversion to give the visitors a 21-10 halftime lead.
Canterbury referee Jamie Nutbrown awarded the penalty when a Stags defender failed to release in a tackle situation.
The Magpies had the bonus point for four tries when Dixon scored his second try in the 47th minute following another lineout drive. Falcon maintained his 100 per cent success rate.
Falcon had the final say with a 67th-minute penalty.
Scorers:
Hawke's Bay Magpies 31 (Ash Dixon 2, Mark Braidwood, Josh Kaifa, tries; Tiaan Falcon 4 cons, pen), Southland Stags 10 (Isaac Te Tamaki try; James Wilson con, pen ). HT: 21-10.