While Spurs play Inter Milan at home in Champions League on Wednesday, on Thursday, Arsenal face a long trip to Ukraine to play Vorskla Poltava in the Europa League, needing a victory to consolidate first place in the group.
The hosts struggled to break down Arsene Wenger's side despite enjoying the majority of possession and will feel hard done by after crafting the best of the game's few openings in a lively game at Stamford Bridge.
Chelsea moved within two points of fourth-placed Tottenham Hotspur in the Premier League after a 1-0 victory over Liverpool thanks to an Olivier Giroud header at Stamford Bridge on Sunday.
Images from Sunday's Premier League action.
Unai Emery begins the task of steering Arsenal into a brave new post-Arsene Wenger world.
Alexandre Lacazette's free-kick sent Arsenal into the Europa League semi-finals with a comfortable 1-0 win away over Napoli, while Chelsea beat Slavia Prague 4-3 in a roller-coaster game, helped by a Pedro brace.
Arsenal fielded a strong team with Ozil installed as captain and the Premier League side soon took control against weakened opposition, given the time and space they will not be afforded when the domestic campaign kicks off in August.
Images from Sunday's action in the English Premier League.
IMAGES from the English Premier League matches played on Sunday
Here are five talking points from the weekend's action:
The 46-year-old has been hired to fill the sizeable void left by the departure of Frenchman Arsene Wenger who had been at the Arsenal helm since 1996.
Arsenal's defence of the trophy ended with something of a whimper as Mikel Arteta's side struggled with repeatedly sloppy defending.
IMAGES from Saturday's English Premier League matches.
On a good night for English clubs in the Europa League, Manchester United hammered AZ Alkmaar 4-0, while Wolverhampton Wanderers also thrashed Besiktas 4-0 in Group K, and Arsenal came from two goals down to draw 2-2 away to Standard Liege and finish first in their pool. The upset of the night came in Group J as Crivelli scored a 90th-minute winner against Borussia Moenchengladbach to send Basaksehir through and knock the Germans out, with AS Roma grabbing the runner-up spot thanks to a 2-2 home draw with Wolfsberger as the Europa League group stage concluded on Thursday.
Premier League champions Liverpool maintained their 100 per cent start to the season with a 3-1 win against Arsenal at Anfield on Monday leaving them level on nine points with pacesetters Everton and Leicester City.
News of all that's transpired on and off the football field
Aston Villa returned to winning ways in stunning fashion as Ollie Watkins scored twice in a 3-0 away thumping of an abject Arsenal in drizzly north London on Sunday.
Ayew strikes as Palace hold Southampton to 2-2 draw
With no Champions League football for a third straight season, the financial realities are starting to bite and Arsenal will be desperate for some of their talented youngsters to come through.
Wenger dropped Rob Holding for the visit to Stoke, preferring Shkodran Mustafi alongside Nacho Monreal and Sead Kolasinac at the back.
Defensive errors were again a common occurrence in the Arsenal backline, but Fiorentina failed to take advantage.
Chilean forward Alex Sanchez returned to haunt his old club with the opening goal in Manchester United's 3-1 victory at Arsenal in a heavyweight FA Cup fourth-round clash.
A late goal by substitute Charlie Austin gave relegation-threatened Southampton a thrilling 3-2 victory over Arsenal on Sunday in new Austrian manager Ralph Hasenhuettl's first home game.
However, one goal proved enough for City who picked up their sixth successive league win to move four points clear of Liverpool, who host Aston Villa later on Saturday, at the top of the standings.
Bournemouth breathed life into their Premier League survival bid on Sunday, coming from a goal down to beat fourth-placed Leicester City 4-1 for their first win in 10 games. Toby Alderweireld's 81st-minute header sealed a 2-1 Premier League victory for Tottenham Hotspur against Arsenal in the first north London derby in their new stadium on Sunday.
Europa League favourites Manchester United secured a 1-1 draw on a threadbare pitch at Rostov, while Olympique Lyonnais beat AS Roma 4-2 helped by a fine individual goal from Nabil Fekir in their last 16, first leg ties on Thursday.
Liverpool continued their perfect start to the season to stay top of the Premier League after a goal in each half gave them a 2-1 victory over Tottenham Hotspur at Wembley on Saturday.
Manchester City have signed French central defender Aymeric Laporte from Spanish club Athletic Bilbao, the Premier League leaders said on Tuesday.
Following is a match by match look at the English Premier League's weekend fixtures:
Arsenal named a strong side captained by Mesut Ozil while Real had Bale on the bench and Eden Hazard, wearing the number 50 shirt, starting alongside fellow new signing Luka Jovic in attack.
Antonio Valencia's early thunderbolt put Manchester United en route to a 4-0 Premier League victory over Everton on Sunday, but they needed a flurry of late goals to finally subdue their unfortunate visitors.
The win allowed second-placed Liverpool to close the gap on league leaders Manchester City to two points.
Arsenal had to come from behind twice to beat Leicester City 4-3 in a thriller as the English Premier League season got off to a flying start on Friday with Arsene Wenger's substitutions turning the match around at The Emirates.
Arsenal's Aubameyang compared to Henry after his derby double
IMAGES from Europa League matches played on Thursday.
Images from the English Premier League matches played on Sunday
IMAGES from Europa League matches played on Thursday.
Tottenham Hotspur claimed a first victory at Chelsea for 28 years with Dele Alli scoring twice in the second half as they came back to win 3-1 and cement fourth place in the Premier League on Sunday.
Arsenal, who fired Unai Emery as manager last week and appointed former player Freddie Ljungberg as caretaker boss, now sit 10th in the table on 19 points, with Brighton a single point behind and three places below them.
Images from Sunday's Premier League matches.