The Portugal international scored twice in seven first-half minutes to secure the win for Slaven Bilic's side, as they made it three wins from as many matches this season.
Gaziantepspor, who sit on the bottom of the table, were unable to cope with the 29-year-old who fired his first home from close range before converting a penalty for his second.
Kasimpasa sat on top of the table until Besiktas' win as they recorded their second win of the season - a 2-1 victory over Konyaspor on Friday.
After falling behind in the fifth minute they were rescued by a 79th minute strike from Sanharib Malki before Ryan Babel scored a dramatic late winner.
Fenerbahce bounced back from their Champions League defeat and European elimination to Arsenal with a 5-2 victory over Sivasspor on Saturday.
Two goals from Dirk Kuyt, one from Pierre Webo and Bruno Alves' first for the club saw Fenerbahce race into a 4-0 lead after 49 minutes.
Aatif Chahechouhe and Cicinho pulled two back for the visitors before Alper Potuk sealed the win in stoppage time.
Galatasaray's frustrating start to the season continued as they were held to a second draw of the campaign on Friday.
Eskisehirspor earned themselves a 0-0 draw at the Ataturk Stadium thanks to an inspired performance from goalkeeper Ruud Boffin.
Other matches on Saturday saw Elazigspor win their first match of the season, 3-1 at Kayserispor, while Bursaspor also won the road, 2-1 at Antalyaspor.
And on Sunday, Karabukspor edged Genclerbirligi 1-0, Rizespor defeated Kayseri Erciyesspor 2-1 and Akhisar Belediye cruised past Trabzonspor 3-0.
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