Liverpool's Uruguayan frontman was virtually unplayable on Wednesday as he illuminated a midweek outing at Anfield.
Suarez plundered four goals against the hapless Canaries - making history as the first man to net three hat-tricks against the same Premier League opposition.
Gerrard - who has played alongside some great players over the course of a distinguished career - believes Suarez is now proving that he deserves a billing alongside the likes of Lionel Messi and Cristiano Ronaldo as the finest performers on the planet.
He told Liverpool's official website: "You have seen a world-class performance, probably one of the best individual performances I've seen at Anfield - and I've been playing here a long time.
"Having worked with him every single day, it's probably less of a surprise to me as it is to the supporters. I've been pushing his corner for a long time that he is up there with the best in the world.
"I think he's getting so close to the main two, Ronaldo and Messi. If he keeps going, I think he can catch them.
"His fourth goal was average and it was a 30-yard free-kick, so I think that sums his performance up."
While Suarez stole the headlines against Norwich, an emphatic victory saw Liverpool as a collective offer the perfect response to Sunday's shock 3-1 reversal at Hull City.
Skipper Gerrard added: "That's what the manager asked for - a big reaction. It was a bad few days after Hull, everyone was down and we weren't proud of the performance.
"We let ourselves down. There have been a couple of occasions this season that we have done it and come unstuck - one was Southampton at home and one was Hull away.
"Hopefully there are not too many more. At home against the teams lower down the league we have been ruthless and that's what we showed tonight. We were ruthless from the first minute.
"It was all about the reaction tonight and the three points. We're really pleased but we've got to match that again against West Ham or tonight is pointless. We have been really good at home, for the majority of games we have been superb.
"There was only Southampton where we haven't turned up. If we keep performing to that level, we can make Anfield a fortress - if you want to be successful in this league, you've got to make your home ground a fortress."