Pep Guardiola celebrated 500 games in charge of Manchester City with a nervy win over Leicester.
Savinho and Erling Haaland gave the floundering defending champions just a second win in their last 10 Premier League games.
It was still not enough to lift them back into the top four, instead leaving them fifth and 11 points behind leaders Liverpool before the Reds' trip to West Ham later on Sunday.
Guardiola had promised not to give up amid the worst run of his managerial career but the visitors lived dangerously at the King Power Stadium with Jamie Vardy twice going close and Facundo Buonanotte hitting the post for the Foxes.
Confidence clearly needs to be rebuilt at City but it was good enough to beat a Leicester side who are fading after a promising start under Ruud van Nistelrooy.
It is now four straight defeats for the Foxes and five in seven games since Steve Cooper was sacked in November which leaves them in the relegation zone.
Vardy had the hosts' best first-half chance, thwarted by Stefan Ortega after Josko Gvardiol's mistake, before Buonanotte's header rebounded off the post but by then they were already trailing to Savinho's 21st-minute goal - his first for City.
Goalkeeper Jakub Stolarczyk, who denied Haaland early, parried Phil Foden's shot and winger Savinho fired in high from six yards.
Leicester still sensed they could exploit City's brittle backline and James Justin came close to a second-half leveller, only for Manuel Akanji to hack clear.
Vardy - who also hit the bar late on - then fired over from six yards before Haaland ended any hopes of a comeback, heading in Savinho's cross with 16 minutes left.