The Bosnian midfielder made his first appearance of preseason after joining from Ferencvaros, but Jackson Martinez ensured that the spoils were shared after Steven Naismith's goal.
The Bosnia and Herzegovina midfielder - signed Monday from Hungarian side Ferencvaros - was brought on after halftime as Everton stepped up its preparations for the new Premier League season.
But the 21-year-old's debut was not marked with a win, as an entertaining affair - which was played as Everton veteran Leon Osman's testimonial to mark his 10 years at the club - ended in a draw.
A mistake from Porto goalkeeper Fabiano gifted Steven Naismith the opener in the 42nd minute but that strike was canceled out by Porto's Colombia international, Jackson Martinez, 12 minutes after the break.
Everton shot stopper Tim Howard was given a run-out after returning from his World Cup exertions with the United States, but his cameo lasted only 19 minutes, with Joel Robles brought on in his place.
After a first half scarce on chances but largely dictated by Porto, Everton took the lead in fortuitous fashion. Fabiano's dismal clearance went straight to Aiden McGeady, who played in Naismith to present the Scot with the simple task of finding the bottom corner.
Besic was brought on at the interval for Ross Barkley, while Osman did his best to create opportunities as the hosts pressed for a second but Porto's quality up front told when Martinez leveled with a neat finish to round off a well-worked move from the Portuguese side.
Both teams spurned chances in the quest for a winner, Porto playmaker Juan Quintero seeing an effort deflected narrowly wide of the post before Osman and defender Tyias Browning going close for Everton, but neither could snatch a second goal, meaning that an even contest finished all square.