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City have 43 points from 20 games with Liverpool on 45 while Newcastle's fourth successive defeat left them 10th in the standings.
Zaire-Emery became the youngest ever French goalscorer in the Champions League at 17 years and 280 days.
Anthony Gordon scored the only goal in Newcastle's deserved 1-0 victory over Manchester United that propelled them up to fifth in the table on 26 points.
Newcastle, who are unbeaten in their last seven league outings, climbed to sixth on 20 points after 11 games
Three-time European champions United, who failed to qualify for the Champions League last season, are third on 72 points with one game remaining.
Eddie Howe's Newcastle are in third place with 70 points and one game to play, four ahead of fifth-placed Liverpool who also have one match remaining. Fourth-placed Manchester United have 69 points with two games left.
Leeds defender Rasmus Kristensen's second-half equaliser denied Newcastle the victory that would have all but assured them a place in next season's Champions League.
City, who have won 10 straight games to catch and then overhaul Arsenal, have 82 points from 34 games with the Gunners on 81 having played a game more.
The defeat also led to Spurs sacking interim coach Cristian Stellini on Monday, with Ryan Mason taking over head coach duties until they find a replacement.
A game billed as a crucial six-pointer in the race to secure Champions League qualification was effectively all over before the clock had reached 10 minutes as fifth-placed Tottenham collapsed like a pack of cards.
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