An injury-hit Besiktas were steamrollered by the Lisbon club who scored their first three goals in a 10-minute spell late in the first half.
Pablo Sarabia wrapped up the scoring early in the second half.
Portuguese champions Sporting are third in Group C, level on six points with second-placed Borussia Dortmund, who they face in Lisbon in their next game. They finish their group-stage campaign at Ajax Amsterdam, who top the group with 12 points.
Besiktas are bottom and without a point.