Olsen slotted a second 40m penalty shortly after the break and this lead was increased when Joe Feast, capping a fine display, backed up a Coast surge from a ruck and crossed the chalk with Olson again adding the extras.
Carterton were again penalised in the ruck and 20-7 quickly became 23-7 when Olson notched his third penalty from wide out in the 55th minute.
Urged on from the base of the ruck by halfback Matt O'Connor, Jordan Carroll and Jimmy Morris added two further tries to the Coast's tally before a late Carterton rally, which saw them camped near the Coast tryline for most of the last 10 minutes, was rewarded when flanker Luke Jones barged over for a try which full back Dan Brown converted.
Carterton manager Jamie Anderson conceded "they were better than us on the day. We had the edge over them in the scrums and lineouts but they were superior in the loose. We coughed up too much ball. Sadly our backs didn't play to their usual standard and allowed them too much space".
In other games, Pioneer made an early statement of intent when they continued their unbeaten run this season, downing Bush Sports 17-3 in Pahiatua. Tipene Haira and Greg Paku dotted down for the visitors with Haira converting both tries and slotting a penalty. A Dylan Bennett penalty was Bush's sole reply.
Elsewhere, Tepanga Isaac and Gareth van Dalen crossed for tries with Hamish Meyrick adding the two conversions and a penalty as Greytown took the honours 17-13 over Gladstone. Guy Wood provided the points for Gladstone with a converted try and two penalties.
Martinborough secured five early competition points by scoring six tries in their 36-8 victory over Eketahuna. Phillip Aporo, Jared Hawkins, Toby Rowlands, Cody Whittaker, Nathan Hunt and Wilba Davies provided the five-pointers with Whittaker adding three conversions. Eketahuna's sole try was scored by Anthony Eagle with Thomas Meuli adding a penalty.
After the first of six rounds, East Coast and Martinborough lead with five points each while Pioneer are in third spot with four. In the Senior Seconds, Puketoi secured a comfortable 41-0 victory over Marist who remain winless this season. Rams defeated Martinborough 43-14 while Tuhirangi overpowered Pioneer 55-0.