The Reds were trailing to Ezequiel Lavezzi's 28th-minute goal in a first half devoid of any real quality on their part.
However, the arrival of Gerrard after the interval completely turned things around and after a couple of near-misses the England midfielder clicked into gear.
Hero: Steven Gerrard scored all three of his goals within 13 minutes
He latched onto a gift from former Liverpool defender Andrea Dossena, whose interception diverted the ball towards goalkeeper Morgan de Sanctis but not with enough pace to prevent the 30-year-old reaching it first.
Gerrard then converted a penalty two minutes from time after Glen Johnson was fouled by Salvatore Aronica and he completed his treble with a delicate dink over De Sanctis.
Captain's performance: Roy Hodgson congratulates his skipper Steven Gerrard after the game
'It was outstanding,' said Hodgson of Gerrard's performance. In the first half we hadn't played that badly and were unlucky to be a goal down to an error which was punished.
'His entry onto the field was a catalyst, it galvanised the crowd and the team and the way he scored the first goal epitomised the energy and the spirit the team showed in the second half.
'We owe a big debt of gratitude to him but he will be the first to join me in saying the whole team in the second half gave a good performance.
'I thought tonight was a real leader's performance - the first goal was not a pretty goal. That was a captain's goal, the goal of a guy who wanted to get his team back in the game even at the risk of injury. That is certainly appreciated by me and my staff.'
All the plaudits naturally went to Gerrard, who was by far the best player on the pitch, but the 30-year-old tried to play down his role.
'We went a goal down and the manager asked me to come on and see if I could help get the lads back in it,' he said.
'Everyone played their part tonight. I'm sure I'll get the headlines but it certainly wasn't just about me.
'Every one of the lads in the second half was just fantastic. For the first goal when you're put in that position against a giant of a goalkeeper you've just got to go in and hope for the best. There was no class involved, just determination and desire and I don't think the keeper fancied it.'
Threesy does it: Gerrard chipped Morgan De Sanctis for his third goal
Napoli coach Walter Mazzarri complained about French official Fredy Fautrel but also criticised his team for conceding 'silly goals'.
'It became increasingly clear in the second half that the referee was happy to whistle for fouls for them and was giving very little to us - this changed the course of the game,' he said.
'But we can't just blame the referee, we were also very naive due to our lack of experience. The first goal was almost like an own goal the way we gave it away and that changed the atmosphere in the stadium. We conceded silly goals.'
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Explore more:People: Glen Johnson, Ezequiel Lavezzi, Roy Hodgson, Steven Gerrard Places: Liverpool, France, United Kingdom