After going down by the same scoreline to Borussia Dortmund in the UEFA Champions League, Galatasaray welcomed newly elected club president Duygun Yarsuvat with a shambolic display.
Marcio Mossoro gave Basaksehir a 16th minute lead and ex- Fenerbahce man Semih Senturk soon doubled the advantage.
Leaders Besiktas, who played the final 23 minutes with 10 men, also lost in dramatic circumstances as Kerim Frei's brace saw them carry a 2-1 lead into the last minute of normal time at Kayseri Erciyesspor.
But their lowly hosts struck through Edinho and Cenk Alkilic to snatch a maiden win of the campaign 3-2.
Sunday's other game was an eight-goal thriller between Trabzonspor and Gaziantepspor.
Visitors Gaziantepspor led thought out from Muhammet Demir's seventh-minute opener but were pegged back to a 4-4 draw in the final minute as Oscar Cardozo netted to offer some respite to under-pressure coach Vahid Halilhodzic.
Fenerbahce are one of four teams one point behind Besiktas and lie fourth after Emre Belozoglu and Dirk Kuyt held their nerve from the penalty spot to seal a 2-1 win at home to Genclerbirligi either side of Liviu Antal's 82nd-minute goal.
Another member of the chasing pack, Akhisar Belediyespor, lost 2-1 at Karabukspor on Friday as Turgay Bahadir struck in the last minute after Ahmet Cebe was sent off for the away team, meaning Theofanis Gekas' eighth goal of the season was in vain.
Bursaspor were the round's big winners as Cedric Bakambu's hat-trick set up a 5-0 demolition of Balikesirspor.
Caykur Rizespor were 1-0 victors at Sivasspor - Leonard Kweuke's 87th-minute winner compounded as the hosts had defender Cicinho sent off in stoppage time.
Torku Konyaspor lost 2-0 to Kasimpasa on Friday, bringing an end to coach Mesut Bakkal's tenure.
