The Londoners were helped by a controversial late decision that denied Stoke an equaliser when the referee ruled a Jon Walters header was not over the line before Peter Crouch cleared the ball.
In other games, Bolton Wanderers won 3-1 at West Ham United, Birmingham City beat Blackburn Rovers 2-1 and newly-promoted West Bromwich Albion edged Sunderland 1-0. Everton were held 1-1 at home by Wolverhampton Wanderers.
Manchester United visit Fulham on Sunday while Manchester City host Liverpool on Monday night.
Seasiders gunned down
When promoted Blackpool beat Wigan in their first game in the top flight for almost 40 years last week they were 3-0 up by halftime but at the Emirates they trailed by the same score at the break and were a man down.
Arsenal had taken the lead after 12 minutes with a nicely-worked Walcott goal and Blackpool's slim hopes disappeared when centre back Evatt was sent off for fouling Chamakh on the edge of the box.
Andrei Arshavin converted the resulting penalty to make it 2-0, Walcott then spun past his marker to bang his second and Abou Diaby rattled in the fourth just after the restart.
Walcott, a surprise omission from England's World Cup squad in June, then produced a dazzling goal when he controlled a Diaby pass, ghosted forward and curled in a precise shot before leaving the field to a standing ovation.
New signing Marouane Chamakh completed the thrashing with his first goal for the club seven minutes from time.
Blackpool coach Ian Holloway was full of praise for the victors. "They are fantastic players, the way they try and play, pass and move is an education to watch," he told the BBC.
"The pace of them shocked my lads a bit but they have to get used to that. I'm just relieved it was only six."
Though Chelsea trounced Wigan 8-0 in May they had lost the away fixture to Roberto Martinez's team earlier in the season and they also looked second-best for the opening half hour on Saturday.
However, when Florent Malouda tapped in the rebound after keeper Chris Kirkland blocked a 34th-minute Frank Lampard shot, everything changed.
Two goals in five minutes early in the second half made sure of the points as Anelka ran on to a John Obi Mikel pass to shoot low past Kirkland and the Frenchman headed in a Didier Drogba cross.
Drogba was the provider again for the next two as Kalou scored after 78 and 90 minutes while new signing Yossi Benayoun rounded things off in stoppage time.