Napoli, who will need a draw in Portugal, were given extra incentive to seek their last 16 ticket when Benfica were held to a 3-3 draw by Besiktas.
Napoli, who will need a draw in Portugal, were given extra incentive to seek their last 16 ticket when Benfica, despite racing to a 3-0 lead, were held to a 3-3 draw by Besiktas in Istanbul.
But despite showing plenty of enterprise in a one-sided game at the San Paolo, Maurizio Sarri's men were forced to settle for a share of the spoils by a Kiev side that showed little interest in scoring goals of their own.
Napoli's second draw in Group B leaves them on eight points, the same as Benfica, with Besiktas in third place at only one point adrift.
"We weren't ourselves tonight," captain Marek Hamsik told Mediaset Premium.
"It's a shame because a win would have made things a lot easier. But we're up near the top of the group and we'll go to Lisbon looking to qualify.
"We know a point will be enough to see us through, but we won't be playing for a draw. More than anything, we have to play better than we did tonight."
Polish striker Arkadiusz Milik's continued absence due to a knee injury meant Belgium midfielder Dries Mertens was pushed up to the main striker's role he has been deployed in for the last few weeks.
But Mertens was one of several Napoli players to have left his scoring boots behind on a night of frustration that saw the hosts whistled and booed off.
Only four minutes after kick-off Mertens was stopped by Artur Rudko when the Dynamo 'keeper came out to clear on the edge of the area.
Napoli were finding space between the Dynamo lines but the pace of Mertens and Lorenzo Insigne was neutralised by their inability to finish.
Rudko was off his line again just after the quarter-hour to thwart Mertens as he ran solo towards goal.
Napoli's luck ran out in comical fashion when Insigne, who broke a seven-month goal drought with a brace at the weekend, tripped over his own feet after collecting Mertens' through ball.
Before the interval Hamsik fired straight at the 'keeper and Insigne wasted another chance when he over-hit a chip for Jose Callejon when Hamsik was in a much better scoring position.
Napoli continued to press but a timely sliding tackle from Yevhen Makarenko stopped Hamsik's daisycutter from reaching Callejon yards from goal seven minutes after the restart.
Napoli went on the counter when Kalidou Koulibaly stole possession in midfield, but with Callejon completely free, Insigne shot straight at Rudko.
Rudko did well two minutes later when Hamsik, from a corner, unleashed a snap shot that forced the 'keeper into a two-handed block.
Sarri replaced Insigne with Manolo Gabbiadini, but despite the fresh legs he, too, failed to find the target.
After hitting a long-distance free-kick in to the defensive wall, Gabbiadini disappointed further by shooting just wide of the far post after collecting Callejon's square ball.
Sarri said: "We still wanted to win this match up until 10 or 15 minutes from the end, and it slipped away from us.
"It's a shame because we could be qualified by now."