Fenerbahce came into the latest round of fixtures as league leaders, but opened the door for Besiktas when they were held to a goalless draw by Trabzonspor on Saturday.
Besiktas took full advantage of their opportunity - Jose Sosa tucking home the opener shortly before the hour mark after some neat build-up play involving Demba Ba.
Sercan Kaya gave the home fans hope when he headed in an equaliser unmarked three minutes later after Rizespor had seen Kivanc Karakas sent off, but Ba had the final say from the penalty spot two minutes from time, with the hosts down to nine following Koray Altinay's earlier dismissal.
The former Newcastle United and Chelsea man sent Serkan Kirintili the wrong way to lift Besiktas a point clear at the summit.
Galatasaray kept up the heat on the top two with a 2-1 win at Eskisehirspor on Monday.
Umut Bulut put the visitors in front after 20 minutes, but they were soon pegged back by an Ibrahim Sissoko leveller.
However, Selcuk Inan tapped home at the far post three minutes from time to earn Galatasaray all three points and pull them within two of the league leaders.
Bursaspor came from behind to claim a 3-1 home victory over Genclerbirligi that lifted them to fourth, above Istanbul Basaksehir, who were denied victory in stoppage time by Karabukspor's Abdou Razak Traore after having Sedat Agcay sent off - the match ending 2-2.
A mid-table clash between Mersin Idmanyurdu and Kasimpasa threw up one of the more eye-catching scorelines of the weekend, with the former coming away 6-2 victors - Welliton taking most of the plaudits after netting a hat-trick.
Basement club Balikesirspor's troubles continue after they were beaten 1-0 at home by Konyaspor, while Sivasspor climbed out of the relegation zone with a 2-0 win against Akhisar Belediye.
In the weekend's remaining fixture, Gaziantepspor won 1-0 at Kayseri Eciyesspor.
