Liverpool took the lead after 19 minutes when Roberto Firmino's scuffed strike found the corner of the net but Dieumerci Mbokani equalised with an audacious back-heel after Liverpool failed to deal with a corner on the half-hour.
Steven Naismith, making his Norwich debut after joining from Everton, beat Liverpool goalkeeper Simon Mignolet with a fierce shot from a narrow angle before halftime and Wes Hoolahan converted a penalty to give the hosts a two-goal cushion.
The unmarked Jordan Henderson then pulled one back for Liverpool with a low shot and Firmino's deft finish from Lallana's cross levelled the scores before James Milner slotted in following a dreadful back pass from Russell Martin.
"A strange afternoon. I was just delighted to get the three points in the end," Lallana told BT Sport.
"When they scored you just think it's going to be one of those days. A massive three points for us.
"That goal was one of those moments in your career that just happens, you go with the flow."
Liverpool manager Juergen Klopp celebrated wildly with his players after the final whistle and his glasses were accidentally knocked off by Christian Benteke in the melee.
"Unbelievable game," Klopp said. "We had a lot of problems today but we played football and scored beautiful goals.
"I think we were the deserved winners in a spectacular game. Of course we were lucky, but we were not too lucky when they equalised in added time. It is very emotional."
It was only the fourth Premier League match to finish 5-4.
"Defensively, it was very poor and that is what cost us," Naismith said. "If 11 men can't defend their goal for two minutes, then you will get punished."
(Reporting by Ed Osmond; Editing by Ken Ferris)
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