Dynamo capitalised on an awful performance from Everton to triumph 5-2 and win the tie 6-4 on aggregate, to progress to the Europa League quarter finals. Romelu Lukaku equalised after Andriy Yarmolenko's opening goal, before Gusev, Veloso, Teodorcyzk and Antunes added a goal each to put the hosts 5-1 up. Everton captain Phil Jagielka offered some late resistance with a header, but it was too little too late for the Toffees.
Dynamo started with intent and took just 90 seconds to create an opportunity, first leg goalscorer Oleg Gusev heading narrowly over the bar from Danilo Silva's looping ball in.
Andriy Yarmolenko started to threaten from the wings, creating a chance for Lukasz Teodorczyk in the area, however the striker's header was soft and caught by Tim Howard.
Yarmolenko did open the scoring soon after with a magnificent goal. He took the ball from the sideline and drove inwards, leaving Leighton Baines behind him before slowing down and curling a superb left footed shot into the top corner of the net. Howard was partially unsighted, but couldn't have done anything to stop the Ukranian player of the year from making it 1-0.
Everton responded quickly, with Ross Barkley's strong run down the left hand side resulting in his accurate shot glancing the post and moving wide. It didn't matter though as Romelu Lukaku equalised soon after, whipping in a screamer of his own to level things up. Lukaku was first to the ball after Christian Atsu had his shot blocked, and curled another left footer into the net, beating Shovkovskiy with ease to increase his tally to 18 goals for the season.
Everton's delight was short lived, as Dynamo raced up the other end to score two quick goals. Awful defending from Antolin Alcaraz allowed Teodorcyzk space in the area as the defender failed to clear with a header, and Teodorcyzk had no problems in smashing the ball past Tim Howard. Just minutes later Dynamo extended their lead through Miguel Veloso. More poor defending from the Blues was punished, as Alcaraz and Jagielka couldn't clear their lines before Veloso's powerful shot deflected sharply off Seamus Coleman and into the net.
Everton came out for the second half knowing that they needed to score and did so positively, with Steven Naismith and Romelu Lukaku both having penalty shouts in the area. They were however rejected, and Everton's attacking play was countered just 10 minutes in as Dynamo added a fourth through Gusev. Yarmolenko continued to dance down the right wing, easily taking on Baines before cutting the ball back for Gusev who gratefully swept the ball into the net.
Everton knew that they needed two goals and perhaps a mircle. Atsu and Barkley attempted to drag them back into the match as the former saw a good strike saved before Barkley hit the woodwork for a second time, a dipping curler hitting the bar as he cut in from the right hand side.
Despite Everton's persistence to salvage something, they knew it wasn't to be as Antunes rattled in Dynamo's fifth of the night with possibly the goal of the night as the clock ticked past 75 minutes. The left back collected the ball out wide, was put under no pressure and smashed a 25 yard screamer into the top corner of the net.
Everton were down and out, however Phil Jagielka's header from a Baines corner saw them gain hope with 10 minutes left. It wasn't to be though as Lukaku saw efforts in the dying stages saved, and Everton crashed out of Europe.
The hosts now progress to the Europa League Quarter Finals, whilst Everton will get back to Barclays Premier League duties knowing that they still have a job to do in order to avoid relegation. The Blues' loss means that there will be no English team in the quarter final of European competition for the first time in 20 years.