Besiktas' 2-0 victory over Kasimpasa on Sunday saw them go a point clear of Fenerbahce at the top, before Ismail Kartal's men drew 1-1 at Bursaspor to leave the sides with identical league records - same points, same goal difference, same number of wins and the same number of goals scored.
Two first-half goals from Demba Ba - the second a penalty - handed Besiktas victory on Sunday, placing pressure on Fenerbahce to produce a result and reclaim top spot.
Dirk Kuyt salvaged a point for the visitors with an intended cross that bounced all the way into the bottom right-hand corner shortly after the hour mark.
And it was one of Halilhodzic's Algerian World Cup stars who gave his new boss the ideal start - Carl Medjani netting two second-half goals before Yusuf Erdogan completed the rout.
Mersin Idmanyurdu missed out on a chance to join Besiktas and Fenerbahce on 20 points as they were held 1-1 by Akhisar Belediyespor.
Batuhan Karadeniz gave Roberto Carlos' men the lead after 25 minutes, before Ronald Vargas pulled level from the penalty spot eight minutes into the second half.
However, Aatif Chahechouhe restored Sivasspor's advantage with another penalty, and Ahmet Aras made sure of a valuable three points four minutes from time after Mehdi Taouil had been dismissed for a second bookable offence.
Karabukspor, meanwhile, remain in the bottom three, despite picking up a 2-2 draw at Genclerbirligi - their first away league point of the season.
In the weekend's remaining fixtures, Istanbul Basaksehir triumphed 2-0 at Rizespor, while Konyaspor beat Gaziantepspor by the same scoreline.
