While Vardy's lone goal saw Leicester hand Chelsea their first home defeat this season, Hodgson's Palace stunned Pep's City 3-2 to end their 100 per cent home record.
Chelsea joined Liverpool and Watford in having a 100 percent record after three games, having previously beaten Huddersfield and Arsenal.
As West Ham scraps to stay in the Premier League, sitting three points above the relegation zone, resentment has grown over the decision to uproot from the Upton Park.
The win lifted United back above Liverpool in the race for Champions League qualification - five days before the fierce rivals meet at Old Trafford.
Raheem Sterling gave City lead inside a minute - he has now scored the earliest and latest goals in the league this season - before Christian Kabasele's own goal and a close-range finish from Sergio Aguero put City 3-1 up.
Playing four days after beating Real Madrid in the Champions League, Tottenham was without forward Dele Alli, centre-back Toby Alderweireld and goalkeeper Hugo Lloris because of injury.
Chelsea have endured a poor start to the season and are currently fifth in the EPL table with 13 points from eight matches. The defeat away to Crystal Palace was their third in the EPL this season.
Lukaku was kept relatively quiet at Old Trafford until the 86th minute when he tapped his 11th goal in 10 games for his new club.
Manchester City has 16 goals in its last three league matches and has a club-record 21 for the season after six games.
Leicester couldn't handle Coutinho's passing and movement in the first half, and only came into the game when he was off the field.
Hodgson's first game in charge of Palace will be against Southampton at home this Saturday.
Palace announced the end of De Boer's 77-day stint in charge in a short statement on Monday.
London: The five-year drought is over. Chelsea is Premier League champion again — with three games to spare.Chelsea's players danced around the field after securing the title with a scrappy 1-0 victory over Crystal Palace
Manchester, England: By mixing attacking verve with defensive resilience, Chelsea has been a class apart in the Premier League and can win the title Sunday with three games to spare.A victory over Crystal Palace at
London: West Bromwich Albion eased any lingering relegation doubts as manager Tony Pulis enjoyed a 2-0 victory Saturday over his former club Crystal Palace in the Premier League.Pulis left Selhurst Park on the eve of
London: Manchester City fell further out of title contention by losing 2-1 to Crystal Palace in the Premier League on Monday, dropping to fourth in the standings and all but surrendering its championship defense.Glen Murray
London: Liverpool's season went from bad to worse on Sunday, when it surrendered an early lead to lose 3-1 at struggling Crystal Palace in the Premier League.After just 12 games, last year's runner-up is failing
Manchester, England: Juan Mata came on as a substitute to score in the 67th minute and give Manchester United a much-needed 1-0 victory over Crystal Palace in the Premier League on Saturday.Just four minutes after
LONDON : Liverpool regained the lead in the English Premier League but the crown slipped further from its grasp as it threw away a three-goal lead in a 3-3 draw away to Crystal Palace on
LIVERPOOL, England : Crystal Palace dented Everton's hopes of Champions League football next season following a 3-2 away win in the English Premier League on Wednesday. The Toffees had slipped into fifth place following Arsenal's
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