Teenager Michael Allan played well at centre-back for the Streamers and Mark Walters made a couple of good saves, but that apart it was a poor performance from the visitors, who had Robbie Skelly sent off late on.
Martin put Preston ahead in the 28th minute, running onto a long ball to lob Walters. He doubled his tally three minutes later, this time rounding the keeper to score from a similar position.
Gary Kennedy made it three shortly after half time with a cross which looped into the far corner before Martin powered home a header in 69 minutes to complete his hat-trick.
Coldstream substitute Skelly was sent off for two bookable offences before Preston sub Ryan Curran slotted home a rebound on 86 minutes to complete the rout.
With a vastly superior over third-placed Gala Fairydean, the managerless East Lothian side need just one point from their last game to be claim second spot. Preston travel to leaders Heriot-Watt University for their last fixture, while Gala, who are five points behind, have two games left.
Streamers have Gala and Eyemouth still to play, but the best they can now finish is fifth.
Coldstream: Walters, McLeod, Kerr (Skelly 79), Allan, M Cornish, Bolton, Armstong (Rutherford 45), Tait, Crawford, Heugh, Simpson (Lamber 45). Subs not used: Turner, Johnson.