Porto dominated for large parts of Thursday's game, but a combination of an incorrect offside decision that ruled out Carlos Eduardo's effort and the outstanding Pepe Reina frustrated them.
There was nothing Reina could do, though, to stop Martinez netting the only goal at the Estadio do Dragao after he reacted quickest to sweep home from 12 yards.
Martinez's 23rd goal of the season in all competitions means Porto travel to Italy for the second leg next week with high hopes of reaching the quarter-finals.
In what was the first European game in charge for interim coach Luis Castro, Porto would have been ahead early on but for a remarkable save from Reina.
Castro's men should have been in front after 19 minutes when Martinez's inviting cross was nodded in by Eduardo, only for it to be incorrectly ruled offside.
The pattern of dominance continued in the early exchanges of the second half when Reina produced another superb stop to acrobatically claw away Fernando's rasping 30-yard drive.
Napoli broke the offside trap and Jose Callejon set up Gonzalo Higuain, whose shot was low and powerful but went through Helton's legs and squirmed wide.
But the game swung Porto's way after 57 minutes when a corner was only half-cleared and Martinez showed great technique 12 yards out to lash home via a deflection.
