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.
"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 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.
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.
