Borussia Dortmund scrape through to the quarters following their 1-2 defeat at home against Zenit St Petersburg

A Robin van Persie hat-trick gave Manchester United a comeback win over Olympiacos on Wednesday while Borussia Dortmund survived a scare from Zenit St Petersburg to reach the Champions League quarter-finals.

Dortmund’s Sebastian Kehl equalised the opening goal from Hulk but Jose Rondon’s header gave Zenit a 2-1 win. However, Dortmund progressed 5-4 on aggregate having won the first leg in Russia 4-2.

“On the whole we deserved to progress and are now at the creme de la creme of European football,” Dortmund coach Juergen Klopp told ZDF.

Manchester United overcame a 2-0 first leg deficit by winning 3-0 on the night thanks to a superb hat-trick from Robin van Persie.

The Dutchman opened the scoring with a penalty and added a second in first half injury time. He then produced the winner with a 51st minute free kick.

The 3-2 aggregate victory is a massive boost for United manager David Moyes who has endured a torrid season since replacing Sir Alex Ferguson.

“The way the players responded after Sunday [was most pleasing],” said Moyes.

“I told the players on Monday morning we have to win 3-0 to give the fans something back. They have been incredible and they deserved it because we’ve not given them many good nights.”

United could have been down and out early on had Hernan Perez not scooped over from the six-yard line from Joel Campbell’s cut-back.

At the other end Rooney was denied when Roberto made a spectacular save to turn his header onto the post.

A crucial point in the game came when van Persie was bundled over in the box by Jose Holebas midway through the first half.

The Dutchman smashed home the penalty himself to break the deadlock and when he sidefooted home Rooney’s cross in first half injury time, the tie was level.

United had keeper David de Gea to thank for a magnificent double save just moments earlier when he denied David Fuster and Alejandro Dominguez.

After the break van Persie completed his hat-trick in the 51st minute with a free kick curled around the wall, deceiving keeper Roberto to find the net.

Perez missed a good chance to head an equalizer from a free kick but Manchester United held on, through a nervous finale, to successfully overturn a two-goal European deficit for the first time since 1984.

In injury time van Persie was stretchered off but after the game Moyes played down concerns over the injury.

In Germany, Borussia Dortmund fell behind after 16 minutes when Hulk cut inside and from long-range sent a high drive flying beyond Roman Weidenfeller.

Dortmund responded with a curling shot from Kevin Grosskreutz which was tipped away by Vyacheslav Malafeev but the keeper could have done more when the hosts levelled in the 39th minute.

A tempting cross from Schmelzer was met by captain Sebastian Kehl who towered to head the equaliser but Malafeev should have done better than help the ball into the net.

Zenit won the match on the night when Rondon stooped to head home Domenico Criscito’s 73rd minute cross but they fell two goals short of completing the turnaround from their first leg loss.