Dynamo arrived in Rotterdam with a goal advantage following a 2-1 home win in the opening match of their third qualifying round fixture, but they had to wait until the dying moments of their away leg before they extended that.
It looked as though the two teams would fight out a goalless draw but, with plenty of added time, Ideye Brown scored in the 96th minute to make certain of the Ukrainian side's passage to the next round.
Belarussian champions BATE Borisov will be joining them in the play-offs following their 2-0 away victory over Debrecen in Hungary.
The two sides drew 1-1 in the first leg of their match, but Dmitri Mozolevski gave BATE the edge after 29 minutes before Aleksandr Volodko added another after 59 minutes.
Germany is one of the top teams ever and they will play the US on Sunday.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.