Newly-promoted to the Premier League, Ipswich had a dream start at the Etihad, but order was quickly restored as City struck three times in four minutes through Haaland and Kevin De Bruyne.
Haaland then fired in from outside the box late on to take his tally since joining City a little over two years ago to 94 goals in 96 starts.
Guardiola said those numbers put the former RB Salzburg and Borussia Dortmund striker alongside the likes of Lionel Messi and Cristiano Ronaldo.
“He did it in Salzburg. He did it in Germany. The numbers are ridiculous," Guardiola told his post-match press conference.
"He can compete in terms of goals with Ronaldo and Messi.
"The numbers are incredible for his age. He’s an incredible threat for us and we’re really happy to have him.
"Hopefully he can be here for many years. That would be really good for us."
Victory takes City top of the table with a maximum six points from the opening two games of their title defence.
There was a mood of celebration before kick-off as City marked their fourth consecutive league title and welcomed back former captain Ilkay Gundogan, who took his place on the bench.
Yet, the champions were stunned with just seven minutes on the clock.
Ben Johnson's pass split a static City defence and Szmodics shot had just enough power to beat Ederson to register Ipswich's first top-flight goal in 22 years.
Kieran McKenna's men have been given a baptism of fire by facing Liverpool and City in their opening two matches and the gap in quality between the Championship and Premier League quickly showed.
The lively Savinho won a penalty on his home debut, which was duly converted by Haaland to level.
Ipswich goalkeeper Arijanet Muric had a return to the Etihad to forget as he was then caught in possession by Savinho, who teed up De Bruyne to roll into an empty net.
Haaland beat Muric to a sumptuous De Bruyne ball over the top and stroked into the unguarded net.
De Bruyne smashed a shot from range off the crossbar as City threatened to run riot.
But to Ipswich's credit they held out for over an hour before Haaland set the seal on another ruthless personal display and three points.
Unlike most of his team-mates who were on international duty at Euro 2024 or the Copa America, Haaland had a summer off and Guardiola believes that has been key to his flying start to the season.
"This season with no Euros and relaxed, he arrived really well," added Guardiola.
"He would have loved to have gone to Euros with Norway. It was not the case.
"Okay, relax, play good this season and try to help Norway qualify for the next tournament."
