Sporting, who sacked coach Ricardo Sa Pinto on Friday, never stood a chance against a confident Porto side who beat Paris Saint-Germain 1-0 in the Champions League on Wednesday.
Martinez opened the scoring after 10 minutes, cushioning a long pass with his knee and, as he turned on goal, applying a neat backheel that left Sporting keeper Rui Patricio stranded.
Argentine playmaker Lucho Gonzalez missed a penalty for Porto and Sporting had Marcos Rojo sent off before Porto's promising Colombian James Rodriguez added a second from the penalty spot with seven minutes to go.
Porto are joint leaders with Benfica on 14 points after six matches, eight ahead of 11th-placed Sporting.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.