Trailing 3-1 from the first leg, the Germans needed a two-goal swing to have any chance of qualification and threw caution to the wind in the second half.
They were rewarded with 20 minutes to go, forcing Kiev defender Evgeniy Khacheridi into conceding an own goal.
Gladbach believed that their dream was alive just eight minutes later as playmaker Juan Arango headed home to make it 2-0 on the night.
That goal seemed to wake up Dynamo and they finally killed off the tie with just minutes left on the clock, Nigerian forward Ideye Brown producing a cheeky chip to give them a 4-3 aggregate lead.
Brown's goal left Gladbach heartbroken, securing the Ukrainian giants a place in Thursday's group stage draw for the first time in three seasons.