A second half Erling Haaland penalty was enough to earn City all three points against Crystal Palace.
The Norwegian sent Vicente Guaita the wrong way from the spot for his 28th Premier League goal of the season after Ilkay Gundogan was felled inside the area.
Haaland's decisive contribution came with 12 to play, earning Pep Guardiola's men a deserved triumph at Selhurst Park.
Rodrigo's stinging volley had forced a smart reaction save from Guaita in the first 45, while Jack Grealish and Haaland in particular also went close before the break.
But the deadlock would eventually be broken by the Norwegian, who took his personal tally up to 34 in all competitions in the process.
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