UPDATE 3-Soccer-Liverpool beat Arsenal in classic to reach semi

(adds details, quotes)

By Mike Collett

LIVERPOOL, England, April 8 (Reuters) - Liverpool beat Arsenal 4-2 in a classic Champions League battle at Anfield on Tuesday to clinch their quarter-final tie 5-3 on aggregate and reach the semi-finals for the third time in four seasons.

Their opponents at the end of the month will again be Chelsea who they defeated at the same stage in 2005 and last season.

In a match that will rank as one of the best played in European competition, Liverpool came back from the dead after Arsenal appeared to have clinched the tie on away goals with only six minutes to play.

But Liverpool's indefatigable belief in themselves on European nights at Anfield saw them turn the tie with Steven Gerrard smashing home an 85th minute penalty and substitute Ryan Babel wrapping up a memorable win with a stoppage time goal.

Arsenal, who were superb for the opening half hour playing football worthy of European champions, took the lead through Abou Diaby after 13 minutes.

Liverpool fought back with a header from Sami Hyypia on the half hour and a stunning shot on the turn from Fernando Torres in the 69th minute to take a 2-1 lead on the night and 3-2 on aggregate.

A breakaway by substitute Theo Walcott which saw him skate past four Liverpool players six minutes from time set up Emmanuel Adebayor to make the score 2-2 -- 3-3 on aggregate and Arsenal ahead on away goals.