The Terrors looked to take a lead to Russia with them but were denied by the last kick of the game in a pulsating encounter at tannadice on Thursday evening
Igor Semshov equalised Willo Flood's opener before Keith Watson slammed home a second for the SPL side.
Alexander Kokorin popped up, however, to bundle home with the last kick of the game and snatch a first-leg lead away from the Terrors.
The game started slowly but Dynamo should have been one up just after 20 minutes. Kevin Kuranyi got in the way of Balazs Dzsudsak’s cross with Zvjezdan Misimovic well placed a tap in.
The German striker was again frustrated as Misimovic played him in with a clever ball, but Kuranyi could only trip over his own feet and ended up flat on his face.
To the dismay of the away side, those two mistakes were to cost the Russians as the hosts notched first on 36 minutes.
John Rankin’s shot deflected off Luke Wilkshire into the path of Flood who slotted home, off the post.
The Scottish outfit could have added to their lead before half-time. First, Johnny Russell skewed his shot wide when he should have done better before Jon Daly headed over Flood’s cross from close range.
Dynamo finally got their communication right in the second half and equalised five minutes after the restart, Semshov rising highest to nod home Alexander Kokorin’s cross.
Radoslaw Cierzniak then came to Dundee United’s rescue with three fine saves in the space of five minutes.
He first stopped Kuranyi’s point blank header, before tipping away Misimovic’s curling effort that was destined for the top corner and finally making a solid save to stop Kokorin’s driven effort.
This seemed to spur the Scottish side on and they were well and truly on the front foot with Rankin skimming a shot just wide whilst Gary Mackay-Steven hit the post after the ball was fumbled by Anton Shunin in goal.
The hosts were back in front with 15 minutes remaining. Mackay-Steven’s corner was headed goalbound by Gavin Gunning but the effort was palmed away by Shunin. Daly reacted the quickest to turn another shot goalwards and after that was blocked, Watson blasted home from close range.
Cierzniak palmed away Kokorin’s effort from a tight angle with three minutes to go as Dundee United were hanging on but they could not hold on for long enough as the same striker’s effort took a wicked deflection off Gunning and past the goalkeeper.
The sides face each other in a week in Moscow with Dynamo holding the away goal advantage.