The 27-year-old attacker notched his second and third goal of the season to help Marcel Keizer’s men extend their winning run to three games.
The visitors started the tie brightly with Bas Dost scoring the curtain raiser five minutes into the encounter from the penalty spot.
Abdellah Zoubir levelled proceedings in the 14th minute before Bruno Fernandes restored Sporting's lead six minutes later.
Former Manchester United winger Nani increased the lead in the 33rd minute, Diaby then scored the fourth goal for his side in the 65th minute.
Bruno Fernandes added to the woes of Gurban Gurbanov’s men ten minutes after and the Mali international completed his brace in the 82nd minute.
Despite the victory they are second in Group E with ten points from five games behind Arsenal and have secured their place in the knockout stages of the tournament.
Sporting take on Rio Ave on December 3 and Diaby will hope to continue the fine form in front of goal.