Watling went on to finish with a bang, slamming 28 runs off the 48th over to bring up his century, which came off 64 balls.
His last 50 runs came from just 13 balls and he finished on 119 not out, which included nine fours and seven sixes.
Dean Brownlie (40 from 47) and Colin de Grandhomme (32 from 27) also produced useful knocks.
Scotland's pursuit never really threatened to challenge New Zealand's total, with Matt Henry (4-26) crippling them early on.
Scott Kuggeleijn (3-47) was also dangerous and, between he and Henry, the match was all-but over in the 21st over after Scotland were reduced to 92-7. The hosts clung on for another 11 overs before Ish Sodhi took the final wicket.
Watling said it was pleasing that New Zealand A had managed to keep momentum after their recent Tri-series victory.
"When you score two centuries in a one-day match, you give yourself a pretty good chance of being on the right side of the result," Watling said.
New Zealand A face Scotland in the second one-dayer tonight (NZT) before finishing their tour with three-day matches against English county sides Kent and Surrey.