Robin van Persie's hat-trick lifted Manchester United to a stunning Champions League comeback against Olympiakos Piraeus  as Borussia Dortmund edged out Zenit St Petersburg to complete the quarter-final lineup.

United, trailing 2-0 from the first leg, won 3-0 at Old Trafford to stay in the hunt for a fourth Champions League title and last season's runners-up Dortmund lost their second leg 2-1 but went through 5-4 on aggregate.

Van Persie cut a forlorn figure as United suffered a humbling defeat by arch-rivals Liverpool in the Premier League on Sunday, but he was back to his lethal best as he picked apart the Greek side who have now lost all 12 matches they have played in England.

The Dutch striker opened the scoring after 25 minutes from the penalty spot after being shoved in the back by Jose Holebas and levelled the aggregate score with a simple tap-in in first-half stoppage time.

Van Persie raised the roof when he curled home a free kick seven minutes after the restart, but the tension around Old Trafford lasted until the final whistle with Olympiakos pushing for an away goal that would have swung the tie in their favour.

Dortmund had done the hard work by winning 4-2 in Russia but the tie threatened to come alive when Zenit forward Hulk beat two men and drilled his team into a 16th-minute lead on the night in Germany.

Dortmund captain Sebastian Kehl settled any nerves when he headed in from close range seven minutes before the break and Zenit never looked like stealing an unlikely win, despite Jose Rondon heading them back in front with 17 minutes remaining.

United and Dortmund joined Chelsea, Real Madrid, Barcelona, Paris St Germain, Bayern Munich and Atletico Madrid in the quarter-finals. The draw for the last eight is on Friday.