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.
Callum Wilson scored in the 2-0 win for the home side.
Casemiro scored in United's 2-0 win at the Wembley on Sunday.
The 31-year-old had been missing since the February 6 earthquake.
Manchester United cemented their top-four place, moving level on points with Newcastle as goals by Casemiro, Luke Shaw and Marcus Rashford sealed a 3-0 victory at Old Trafford.