There were wins for Manchester United, Leicester and Bournemouth, but fellow Premier League team Crystal Palace came unstuck in losing 4-1 at second-tier Bristol City.
Arsenal boss Arsene Wenger celebrated his 68th birthday in style as the Gunners demolish the Toffees, Koeman's team in the relegation zone.
With several young players, including Reiss Nelson, Joseph Willock and Ainsley Maitland-Niles, the Gunners didn't look dangerous until Giroud's goal.
Watford jumped into the top four with its first home victory of the season, maintaining its excellent start under new manager Marco Silva.
Arsenal extended its unbeaten run in all competitions to seven matches to move up to fifth in the standings.
Within 25 minutes, Arsenal was a decisive 3-0 up through two goals by Theo Walcott and Rob Holding.
It was a disappointing way for West Brom midfielder Gareth Barry to celebrate making a record 633rd Premier League appearance.
Chelsea, Manchester United, Manchester City, Arsenal and Everton advance to the last 16 despite fielding virtual second-string lineups.
It was the most explosive moment of a largely sedate lunchtime fixture with Arsenal transformed from the side that collapsed so meekly to lose 4-0 at Liverpool on top of a defeat to Stoke.
Four of City's goals against Liverpool came after Sadio Mane was sent off for a high challenge that forced goalkeeper Ederson off injured in Manchester.
Gunners managed to claim three points after their heavy losses to Stoke City and Liverpool.
After suffering back to back defeats in the World Cup qualifiers to Bolivia and Paraguay and a thumping defeat to Liverpool in the EPL, Sanchez bashes the Pundits for their criticism.
Mbappe has been added to a glittering assembly of attacking talent that includes Brazil star Neymar, striker Edinson Cavani, and wingers Angel Di Maria and Julian Draxler.
Sanchez was linked to Manchester City but Arsenal ensured that the move fell through at the last minute.
Arsenal's team remains as multi-national as ever, with two French strikers, midfielders from Germany, Chile, Switzerland, Spain and Egypt, and defenders from Spain, France, Germany and Bosnia-Herzegovina.
Facing the prospect of losing Oxlade-Chamberlain on a free transfer next year, Arsenal instead secured a big fee for the England international.
Arsenal were overrun from the start and crumbled to goals from Roberto Firmino, Sadio Mane, Mohamed Salah and Daniel Sturridge.
Mesut Ozil delivers a heartfelt apology to the Arsenal fans on social media after the Gunners were humiliated by Liverpool at Anfield 4-0.
Even after conceding, Arsenal remained as chaotic and lethargic, never looking capable of mounting a comeback.
Liverpool said this week that Coutinho was also ill. He will miss the English Premier League game against Arsenal on Sunday.
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