The Ukrainians were heading out of the competition when Terrence Boyd fired Rapid ahead after just six minutes.
The home side's reply was swift, however, and goals from Jeremain Lens and Oleg Gusev before the half-hour sent them on course to the last-32 before Miguel Veloso added a 70th-minute free-kick.
Rapid grabbed their early advantage, and provisionally move above Dynamo and into second place in Group G, through their Germany-born, United States international Boyd.
Marcel Sabitzer fed a pass to Guido Burgstaller and his right-wing delivery was perfect for Boyd to fire beyond Olexandr Shovkovskiy from six yards.
Dynamo's response did not take long to come and they gave warning an equaliser was on the way as Lens forced Rapid goalkeeper Jan Novota into action before Ognjen Vukojevic shot over.
Lens was flagged for offside as he tried too eagerly to get in behind the defence but when he did hold his position the leveller arrived on 22 minutes.
The Holland international chested down Vukojevic's pass from the right flank and scored into the bottom right-hand corner.
At 1-1 that was enough to ensure Dynamo's passage but a second six minutes later gave them breathing space.
Gusev got the goal but it owed to Brown Ideye's determination to keep the ball in before laying the ball back for him to net from six yards.
An entertaining first half could easily have finished 2-2, though, as Shovkovskiy made an excellent block to deny Stefan Hofmann before Sabitzer curled wide.
Andriy Yarmolenko could have made it 3-1 to Dynamo a minute after the re-start when he shot wide from six yards, but the hosts would have their two-goal lead 20 minutes from the end.
Veloso whipped his 20-yard free-kick over the wall and into the bottom right of the goal to make Dynamo's progress certain.
Novota did well to limit any further damage as he superbly kept out a Younes Belhanda effort while Dudu was off target from six yards in the closing moments.