UEFA Europa League: Dynamo Kiev 1 Fiorentina 1
It appeared as though Fiorentina's wastefulness would prove costly as Jeremain Lens' deflected effort put the hosts into a 1-0 half-time lead.
But Babacar, who replaced Mario Gomez in the 77th minute, provided a neat overhead finish in the second minute of injury time to earn a well-deserved draw.
Vincenzo Montella's men were seeking a swift response to back-to-back 3-0 defeats against Juventus and Napoli that saw them eliminated from the Coppa Italia and their Champions League hopes severely damaged.
The Serie A side caused plenty of problems in the first half at the Olimpiyskiy National Sports Complex, with Mohamed Salah and Matias Fernandez coming the closest.
It was Dynamo - who are unbeaten at the top of the Ukrainian Premier League - who led at the break, though, thanks to Lens' strike, which took a kind touch off Nenad Tomovic.
But it was not to be for Sergei Rebrov's side as Babacar had the final say.
The home team were subject to a partial stadium ban due to racist behaviour of fans in the last round against Everton, but there was plenty of atmosphere in the Ukrainian capital.
Fiorentina looked to quieten the supporters and started much the brighter. The lively Salah led a three-on-two break before picking out Joaquin on the left, and he cut inside but saw his shot expertly blocked by the sliding Yevhen Khacheridi - the visitors' calls for a penalty falling on deaf ears.
Dynamo were dealt a blow when Vitorino Antunes limped off in the 24th minute, Salah shooting tamely at Oleksandr Shovkovskiy from a good position soon after.
Fiorentina continued to create the better chances and Fernandez played a neat one-two with Gomez before curling wide of the right-hand post from the edge of the penalty area.
The Italians' profligacy was punished as Dynamo broke the deadlock nine minutes before the break.
Lens cut in from the right and his speculative effort clipped the heel of Tomovic and looped over Norberto Neto in the Fiorentina goal.
The start of the second half saw Fiorentina once again look the more threatening, although their final delivery was letting them down.
Dynamo were perhaps lucky not to concede a penalty in the 58th minute when Borja Valero was bundled to ground by Domagoj Vida.
Valero then saw a header hit the outside of the post when he did well to turn Marcos Alonso's cross goalwards in the 76th minute.
But Fiorentina finally got the goal their play deserved when Dynamo failed to deal with Fernandez's cross from the right and Babacar took advantage of the uncertain defending to hook the ball into the net from point-blank range.