Podolski had fired a spectacular 81st minute equaliser to wipe out Jakub Blaszczykowski's opener for Borussia.
Turkey midfielder Sahin and Germany forward Podolski clashed in the last minute following a late tackle by the Cologne player, earning a booking for both.
Podolski then held three fingers up to remind Sahin that Germany beat Turkey 3-0 in last week's Euro 2012 qualifier in which both played.
But Sahin had the last laugh when he scrambled the winner, then slid right past a despondent Podolski with his finger in the air to celebrate.
"I don't want to make a big thing of it," Sahin said in the post-match touchline interview. "I was a bit emotional."
Borussia moved on to 21 points from eight games and overtook Mainz 05 on goal difference.
Borussia went ahead in the 20th minute when Shinji Kagawa's cross was met by Lucas Barrios and the Paraguay forward's header bounced off Blaszczykowski and into the net.
Cologne gave goalkeeper Miro Varvodic his Bundesliga debut in place of 39-year-old Colombian Faryd Mondragon and he set up the equaliser.
Varvodic's long free kick into the Borussia area was only partially cleared by defender Mats Hummels and landed at the feet of Podolski, who rifled in a left-foot shot from just outside the penalty area.
Sahin provided the final twist on a rainy night, exchanging passes with Robert Lewandowski to score the winner from six metres in the first minute of stoppage-time.
