With the ball, spin trio Amelia Kerr (2/13), Leigh Kasperek (2/27) and Eden Carson (1/19) led the way, as no Sri Lanka batter made more than 35.
Kerr’s two wickets takes her tournament tally to seven from three matches, two behind South Africa’s Nonkululeko Mlaba, albeit with her having played one less match.
While she didn’t pick up any wickets, Rosemary Mair set the tone at the top of the innings by conceding just 17 runs from her four-over spell.
Sri Lanka’s best score came from captain Chamari Athapaththu, despite taking 41 balls at a strike rate of just over 85.
In reply, Plimmer played second fiddle in an opening stand worth 49 with Suzie Bates (17 off 22 balls), the highest partnership of the match.
Once Bates fell, bowled by Sachini Nisansala in the eighth over, Kerr added runs to her display with the ball and scored an unbeaten 34 to guide New Zealand home.
Plimmer was patient and reached her 50 from 41 balls, with just 16 runs coming from boundaries.
At 95/1 and with victory in sight, Plimmer departed when she holed out to deep midwicket off Athapaththu, but left the field having all but completed the run chase for her side.
The half-century was Plimmer’s second in a New Zealand shirt, and equalled her career international high score of 53 scored against Australia in Brisbane earlier this year.
With a handful of runs required, captain Sophie Devine arrived at the crease and plundered 13 from eight balls, including the only six of the match, to guide the White Ferns to victory.
While also hoping for a convincing Australian victory over India, New Zealand will also need to overcome Pakistan in their final group-stage match, played on Tuesday morning (NZ time).
Sri Lanka 115/5 (Athapaththu 35; Kerr 2/13, Kasperek 2/27)
New Zealand 118/2 (Plimmer 53, Kerr 34 not out; Athapaththu 1/8)
Alex Powell is an Online Sports Editor for the NZ Herald. He has been a sports journalist since 2016, and previously worked for both Newshub and 1News.