Traditional powerhouses Galatasaray, Fenerbahce and Besiktas all failed to win in the second round of fixtures following victories to start the new campaign.
Defending champions Fener were held to a 0-0 draw at Trabzonspor, while arch-rivals Gala produced the same result against Eskisehirspor.
Besiktas were able to find the net as midfielder Olcay Sahan spared their blushes with a goal nine minutes from time to earn a 1-1 home draw with Rizespor, who had taken the lead in the 48th minute through Umit Korkmaz.
Bursaspor and Konyaspor were the only teams to claim success in a second week of action that was dominated by stalemates.
Second-half goals from Volkan Sen and Fernandao were the difference as Bursapor came from behind to win 2-1 at Genclerbirligi, while Konyaspor beat newly promoted Balikesirspor 2-0.
That result leaves Balikesirspor still waiting for their first point of the season, but fellow newcomers Mersin Idmanyurdu are on the board following a 2-2 draw at Kasimpasa.
A first-half double from attacker Melih Gokcek looked to have sealed the points for Idmanyurdu, however, Adem Buyuk equalised in the 83rd minute for Kasimpasa after Sanharib Malki had pulled one back.
There was late drama in Manisa as Akhisar Belediyespor drew 2-2 with Sivasspor.
Midfielder Aatif Chahechouhe appeared to have earned a 2-1 triumph for Sivasspor with his second goal in the 90th minute, only for Greece striker Theofanis Gekas to double his tally just two minutes later to salvage a point for the hosts.
Elsewhere, Istanbul Basaksehir continued their unbeaten start to life in the top flight with a 0-0 draw at Karabukspor and Gaziantepspor played out a 2-2 tie with Kayseri Erciyesspor.
