ReutersMartinez towered above Academica's defence and headed in the winner with 90 minutes on the clock to sealed a perfect debut start for the Colombia international.
Coach Vitor Pereira kick-started the season with a trophy, his third for the Portuguese Premier League champions since taking over from Tottenham Hotspur manager Andre Villas-Boas just over a year ago.
Academica, who won the Portuguese Cup in May with a shock victory over Sporting, were sturdy in defence and contained Porto for most of the game until succumbing to Martinez's well-taken header.
