The Ukrainian champions advance thanks to Chelsea's 2-0 win over Porto at Stamford Bridge.
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The home side thought that they had got off to the dream start when Garmash poked home inside two minutes, only for his goal to be ruled out for offside.
Dynamo did take the lead, however, when Maccabi failed to deal with a Serhiy Rybalka free kick from the right wing, with Garmash prodding home at the near post after Tal Ben Haim had sent the ball crashing against the woodwork when trying to cut out the cross.
With results elsewhere crucial to Dynamo's hopes of qualification, there was a nervy atmosphere inside the NSK Olimpiyskyi.
Ben Haim, eager to make amends for his earlier error, carved out a goal-scoring chance when he burst down the wing and sent a dangerous cross into the box just before the hour mark, but there was no teammate on hand to tap home.
Rybalka could have wrapped it up with his late strike from range, but Predrag Rajkovic got everything behind it.
The result means that Rebrov's side finish second in Group G, and advance to the last 16 for the first time in 16 years.