Savinho arrowed in his first goal for the club in the 21st minute, pouncing on a rebound after Leicester's stand-in goalkeeper Jakub Stolarczyk failed to hold Phil Foden's strike.

The Brazilian then turned provider for Haaland to head in a decisive second with 16 minutes remaining, delivering an excellent cross for the Norwegian to nod back across goal and in.

Leicester had its chances against a vulnerable-looking City defence, with Jamie Vardy slicing over from its best opportunity, and its profligacy was punished.

Ruud van Nistelrooy’s team stays 18th on the table, while City moves to within four points of fourth-placed Chelsea, which faces Ipswich Town on Tuesday (AEDT).

Guardiola was overwhelmed with a sense of relief, rather than joy, after the victory, his side's first win in four league games since beating Nottingham Forest on 5 December (AEDT).

“I would say we needed it, all of us,” Guardiola said.

“It’s not the ideal performance but in these moments it’s almost impossible.

“It’s important to win here, always we struggled. We don’t have enough energy to sustain our game for 90 minutes but hopefully this result, in the new year, will help us to bounce back from the bad results and our players will come back.

“It’s not enjoyable, it’s just relief right now. That is the real word to express the feeling that we have in all of us.

“It looks like we have done incredible things for many years, and now we were not able to win games. It’s just a fact of relief, but we have to improve.”