Both teams went into the game having registered a single point each from four group games and the main action on Thursday saw the visitors' Aleksandar Mitrovic, who came on as a half-time substitute, score the equalising goal before being sent off.
The home side had gone ahead after nine minutes through Flavinho before Mitrovic levelled with 25 minutes to go only to be shown a red card for violent conduct 10 minutes later.
Neftchi started the game the stronger and had their first chance after four minutes but Julius Wobay sent his shot over the bar.
The home side then went ahead with a fantastic effort from Flavinho who drilled in a shot from 25 yards which found the top right corner of the goal.
It took 15 minutes for the visitors to create their first chance but Sasa Ilic's cross was headed wide by Stefan Scepovic.
Partizan won two corners in quick succession, the second presenting a chance for Milos Jojic to shoot but his effort was off target.
Neftchi's Javid Imamverdiyev wasted a good opportunity to extend the lead when he fired over the bar from 12 yards and then saw another effort cleared by Ivan Ivanov.
Just before half-time the home side's Rashad Sadygov fired wide left but there was still time for Partizan's Scepovic to put his own effort off target.
Early in the second half, as the visitors continued to press, Aleksandar Miljkovic volleyed over the bar before Milos Jojic also failed to find the target.
But the pressure finally told as Partizan equalised with 25 minutes to go as Mitrovic shot home after being set up by Ilic.
But 10 minutes later Mitrovic was dismissed for violent conduct in an incident which saw two other players booked.
Both sides pressed to find a winner but had to settle for a share of the points.