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.
Mossoro notched a second in the 69th minute before Doka Madureira completed the rout and Galatasaray coach Cesare Prandelli shunned post-match media duties having been barracked by his own supporters.
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.
Mersin Idmanyurdu are up to second thanks to a 4-2 victory at home to Eskisehirspor, who slip into the bottom three.
Oktay Delibalta bagged a brace for Mersin, whose win was all the more remarkable given they were 2-0 down during the first half and still a goal behind when Murat Ceylan was sent off on the hour-mark.
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.