The strength of the wind was highlighted by a clearing kick made 10 metres ahead of the Wesley tryline travelling the entire field to go dead at the other end.
The resulting scrum gifted Lindisfarne their first real attacking opportunity just before halftime.
Impressive No 8 Patrick Tuifua got over the tryline but was held up with the final play of the half.
Lindisfarne were much better playing with the wind in the second half, but it was Wesley who made it 24-0 just a few minutes after the break.
Ben Ofa broke three tackles and then threw an outstanding offload to reserve hooker Oscar Aloua for their fourth try.
The hosts were finally able to build some consistent attacking pressure but largely struggled to execute and turn that into points.
They did get a consolation try to winger Harry Kirkpatrick about 10 minutes into the second half, but Wesley's defence kept them out for the rest of the game.
St John's College also lost their second straight game of the Central North Island competition at home, 48-20 to Feilding High School.