Alan Irvine's side have struggled to find any form after returning from a tour of the United States and that continued on Saturday as they were comprehensively beaten by their Primeira Liga opponents.
Martinez struck twice in three second-half minutes as Julen Lopetegui maintained his unbeaten run in charge of Porto, who enjoyed ideal preparation for their opening domestic clash against Maritimo on Friday.
Jonas Olsson claimed Albion's solitary goal in what could have been an even heavier defeat had Porto taken late chances, and Irvine has plenty to contemplate ahead of his team's Premier League curtain-raiser with Sunderland next Saturday.
The opening goal came midway through the first half after poor defending from West Brom at a corner allowed the ball to drop to Casemiro, who had the simple task of tapping into an empty net.
West Brom worked hard to get themselves back into the game and got their reward five minutes before the break as Porto gifted Olsson the equaliser with similarly poor marking from a corner.
After Craig Dawson failed to meet Chris Brunt's delivery, the Swedish defender glanced a header home, squeezing it between a defender and the post.
Martinez made his first impact on the game six minutes into the second half when Dawson misjudged a clearance from Ricardo Quaresma's cross and was punished by an emphatic finish.
The forward then doubled his tally in the 54th minute as he got in front of his marker to meet a left-wing cross and volley past Ben Foster.
Quaresma and Alex Sandro each had chances to extend Porto's lead in the final 20 minutes, but found Foster equal to their powerful respective efforts.
A late rally from Albion saw Craig Gardner waste two opportunities as Irvine's men slipped to defeat.