The Wanderers came from behind and held on after playing the last half-hour with 10 men following the dismissal of goalkeeper Jarrad Tyson.
Argentine Martinez scored the go-ahead goal after Western Sydney had trailed 1-0 and Nicholls was involved in the build-up to two of the visitors' scores.
The match started in sensational fashion with both sides scoring in the first six minutes.
Blake Powell slammed home a cross from Storm Roux to give the Mariners a fifth-minute lead.
Within 60 seconds, it was the turn of the Wanderers' travelling supporters to celebrate, with Japanese winger Jumpei curling the ball home.
Each goal was aided by a slight deflection.
The Wanderers had the better of the next 20 minutes and deservedly hit the front when Martinez's diving header rounded off a fine team move featuring good work from defender Jack Clisby and Nicholls.
The Mariners finished the half well with Roy O'Donovan hitting the post and Adam Berry blazing the loose ball over.
Western Sydney went close a couple of times before Nichols and Scott Neville combined down the left-hand side, and Mariners defender Jake McGing turned a cross from the latter into his own net.
Tyson was sent off by referee Kris Griffith-Jones who deemed the keeper had denied Trent Buhagiar a goalscoring chance.
The Mariners' Harry Ascroft had a shot saved by substitute goalkeeper Andrew Redmayne.
But, the Wanderers created all the final-quarter opportunities with Martinez, Clisby and Nicholls having shots before substitute Brendon Santalab lashed home a cross from Neville for the fourth goal.
