The Ukrainians opened the scoring with a terrific volley but they were denied all three points by the concession of a penalty in the dying seconds of injury time
A technically excellent volley by Andriy Yarmolenko gave Dynamo the lead on the stroke of half-time, but Ivan Krystanovic grabbed the hosts their first point in the competition by netting a penalty in the 95th minute.
Cold and snowy weather in Zagreb made for an almost complete absence of passing football, with most of the players relying on long balls to find their team-mates. The few Dinamo supporters on hand, however, showed great spirit and created a fiery atmosphere at times with their incessant chanting, despite the freezing conditions.
Assistant coach Olekiy Mykhailychenko was in charge of the Bilo-Syni, as trainer Oleh Blokhin is currently struggling with health issues. He had to leave behind injured attacking-midfielder Niko Kranjcar, who spent most of his youth career at the Croatian club.
On the hosts' side, Zagreb's new coach Krunoslav Jurcic joined the sidelines, following the departure of Ante Cacic, who was in charge at the capital for only one season. Manchester City target - 16-year-old Alen Halilovic - started on the bench.
An early opportunity in the second minute by Brazilian striker Sammir showed that Zagreb were desperate to end their 11-game losing streak in the tournament and finally get some points on the board. The weather made it impossible to create any chances, though, with the ball constantly getting stuck in the snow.
Then, in the ninth minute, the encounter was suspended by the referee as the snow became unbearable. The nearly invisible pitch markings were then cleared.
Forward Duje Cop then had a great chance when play resumed after Ukrainian goalkeeper Maksym Koval failed to hold on to the slippery ball. The Croatian international, however, could not do better than hit the woodwork.
Another close call for Zagreb followed in the 18th minute, when a back pass to Koval got stuck in the snow and he almost deflected the clearance into his own goal via the body of Sammir.
Meanwhile, at the other end, the visitors nearly grabbed the opener. A powerful shot by Ideye Brown stopped instantly on the bounce in the 20th minute and the snow prevented it from getting the momentum to roll into the net.
However, the Ukrainians were able to finally open the scoring on the stroke of half-time. Yarmolenko, who received the ball from Denys Garmash, landed a superbly volleyed chip from the edge of the penalty area over Kelava onto the undeside of the bar and then into the net.
During the second half, the pitch became increasingly more playable as the snow turned into more of a slush. However, both teams rarely made use of the improved conditions and maintained the long ball game.
In the 65th minute, Fatos Beqiraj missed a big chance of ending his sides' goal drought in this group stage, when he bore down on goal but lacked the composure at the crucial moment.
Krystanovic finally was able give the fans something to shout about, however, when he scored a penalty in the 94th minute.
Nothing changed with the result, as both teams went into the match with their respective fates already sealed. Having scored only a single point in their Champions League group matches, the Plavi had no chance to escape the bottom of Group A, while the Ukrainians, who remain third, are now set for Europa League action.