The combative 21-year-old arrived from Ferencvaros this summer for a fee of £4 million, signing a five-year deal at the club, and did well as his tough tackling, harrying play helped Everton to a 1-1 draw against the Portuguese giants.
Roberto Martinez was very impressed with his new signing, telling the Everton website: "I thought Besic looked like someone who had played here for years. That's what I saw at the World Cup - someone who is never fazed."
Goodison Park also saw the return of Romelu Lukaku, with the Belgian paraded in front of the Toffees faithful having this week completed his record breaking £27 million move from Chelsea.
Osman himself was afforded plenty of credit, with a late withdrawal giving him a chance to milk the applause of the home crowd.
Will Besic be a good signing for Roberto Martinez's men?