Ismail Kartal's side have not been top of the table since the opening weekend, but the win at the Ataturk Olympic Stadium sees them climb above Galatasaray.
Emmanuel Emenike opened the scoring after just three minutes of the Istanbul derby, converting Alper Potuk's low cut back beyond goalkeeper Tolga Zengin.
Three goals in 13 second-half minutes from Josue, Volkan Sen and Fernandao sealed the three points for Senol Gunes' side, while Sivasspor finished the game with 10 men after Burhan Eser's late dismissal.
John Chibuike's third goal of the campaign was enough to give Gaziantepspor a 1-0 win over Mersin Idmanyurdu, but Istanbul Basaksehir were unable to follow last week's win over Galatasaray.
Having won 4-0 in their previous game, Abdullah Avci's side fell to a 1-0 defeat at the hands of Genclerbirligi, Nemanja Tomic's 95th-minute winner securing victory.
Konyaspor lifted themselves away from the bottom three with thanks to a 1-0 victory over Karabukspor, while Balikesirspor rescued a 2-2 draw with Eskisehirspor thanks to Nuno Coelho's late equaliser.
