Early goals from Pedro and Alvaro Morata gave the team the perfect start to boss Maurizio Sarri’s first home Premier League game.
Arsenal stormed back in the pulsating London derby and were level by half-time courtesy of goals from Henrikh Mkhitaryan and Alex Iwobi.
As the Gunners continued to threaten in the second half, Sarri made a double substitution on the hour mark, bringing on Eden Hazard and recent signing, Mateo Kovacic for his debut.
And Hazard set up the winner, breezing past Alexandre Lacazette on the left and crossing low for Alonso to fire home.
Alonso had set up Chelsea’s ninth-minute opener, racing onto Jorginho’s clever pass and squaring the ball for Pedro to score with ease.
Arsenal responded and Pierre-Emerick Aubameyang was denied by a near-post save from keeper Kepa and then, a minute before Chelsea doubled their lead, squandered a glorious chance to haul Arsenal level.
Matteo Guendouzi opened Chelsea’s defence with a clever pass out to Hector Bellerin, whose right-wing cross perfectly teed up Aubameyang only for the striker to side-foot over.
It proved to be a costly miss for the Gunners, who were undone again when Morata chased Cesar Azpilicueta’s ball forward, got the better of Shkodran Mustafi and slotted past former Chelsea keeper Petr Cech.
England duo Harry Kane and Kieran Trippier were on target against Fulham
Earlier, Harry Kane ended his August goal drought and Kieran Trippier scored a stunning free-kick as Tottenham beat Fulham 3-1, while there were also wins for Leicester, Everton and Bournemouth.
Lucas Moura’s opener just before half-time at Wembley Stadium was cancelled out by Aleksandar Mitrovic, who headed in Fulham’s first goal back in the top-flight to equalise.
But Trippier’s long-range effort, which was reminiscent of his goal for England in the World Cup, and a third from Kane, who had not previously scored a Premier League goal in August in his 14 previous games, secured the win at Wembley.