Pedro Goncalves broke the deadlock with a penalty goal in the 31st minute at Estadio Jose Alvalade in Lisbon.
After seven minutes, Goncalves scored another goal, while João Paulo Dias Fernandes netted Sporting CP's third goal in the 41st minute.
The fourth goal came from Pablo Sarabia.
Besiktas' Brazilian midfielder Josef de Souza was shown a red card in the 90th minute.
In another group C match, Ajax defeated Borussia Dortmund 3-1 at BVB Stadion Dortmund.
Ajax currently top the group with 12 points while second-place Borussia Dortmund and third-place Sporting CP have collected six points each.
Besiktas are at the bottom of Group C without a single point.
Wednesday's results:
Sporting Lisbon (Portugal) - Besiktas (Turkey): 4-0
Manchester City (England) - Club Brugge (Belgium): 4-1
Leipzig (Germany) - Paris Saint-Germain (France): 2-2
Liverpool (England) - Atletico Madrid (Spain): 2-0
AC Milan (Italy) - Porto (Portugal): 1-1
Borussia Dortmund (Germany) - Ajax (Netherlands): 1-3
Real Madrid (Spain) - Shakhtar Donetsk (Ukraine): 2-1
Sheriff (Moldova) - Inter Milan (Italy): 1-3
