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Klopp confirmed the 26-year-old would not play during the busy festive period when Liverpool play three times in eight days.
The win restored Liverpool's 11-point advantage over second-placed Leicester City.
Fourth-placed Chelsea suffered a shock 2-0 loss at home to Southampton while Harry Kane and Dele Alli were on target as Tottenham Hotspur came from behind to beat Brighton & Hove Albion 2-1.
The willingness to fight until the very final minute is quintessential City. This quality has won them four of the last ten League titles.
It was another impressive performance from Chris Wilder's promoted side, who were unbeaten away in the league, but in the end third-placed City's sharpness in front of goal was decisive as Guardiola picked up his milestone 100th Premier League win.
Klopp took Liverpool to the brink of their first ever Premier League title last season, finishing a point behind champions Manchester City.
Guardiola had said prior to the game that City could not afford reinforcements in January, despite spending less than rivals in the summer transfer window.
Manchester United earned a first victory since the opening weekend by beating Leicester City 3-1, while Chelsea and Tottenham Hotspur registered emphatic wins.
Harry Kane's eighth goal in six Premier League games against Southampton steered 10-man Tottenham Hotspur to an unlikely 2-1 victory after errors from his team mates on Saturday.
Liverpool's win was their 16th in succession in the league and extends their lead at the top to eight points ahead of champions Manchester City's trip to Everton later on Saturday.
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