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Arsenal stayed a point ahead of Manchester United in the race for the Champions League by thrashing Bournemouth to earn their eighth straight Premier League home win.
Mesut Ozil, recalled to the side, fired the Gunners ahead before he set up Henrikh Mkhitaryan to sweep in.
A defensive mistake allowed Bournemouth to pull a goal back through Lys Mousset's simple finish, but any hopes the visitors had of ending a miserable run of eight successive league defeats on the road quickly ended after the break.
Skipper Laurent Koscielny blasted in off the post following a set-piece, then Pierre-Emerick Aubameyang added another when he was given the space to race clear and calmly slot in.
Substitute Alexandre Lacazette sealed victory with a sublime free-kick as Arsenal warmed up for Saturday's north London derby in style.
Spurs' defeat at Chelsea leaves Arsenal now four points behind their arch-rivals, with a buoyant Emirates Stadium warning "Tottenham Hotspur, we're coming for you!" as they celebrated a rampant win.
Bournemouth's visit was seen as a must-win by Gunners fans with, what would should be, trickier tests to come against Spurs and Manchester United in their next two Premier League games.
These matches - plus the two-legged Europa League last-16 tie against Rennes - look set to define manager Unai Emery's first season at the helm.
A healthy points haul against Spurs and United would consolidate the Gunners' place in the top four as they head into the final stretch.
But failure to beat either would leave the race for the Champions League - which Arsenal have missed out on for the past two campaigns - wide open.
Did Ozil impress on his Premier League recall?
Ozil, 30, has become somewhat of a peripheral figure at the Emirates under Unai Emery this season, making just 14 league starts and often left out of the side because of concerns from the Spaniard about his form or fitness.
The German was restored to the starting line-up against Bate Borisov in the Europa League last week and made a decent impression when he came on as a substitute against Southampton on Sunday.
That led to Emery giving another opportunity to the club's star name, and highest-paid player, against Bournemouth - and Ozil repaid him with a classy performance in what was only his second start of the year in the Premier League.
The former Real Madrid midfielder lined up in a central attacking midfield role, alongside Mkhitaryan and behind Aubameyang, linking up to both players with good effect.
Arsenal made the perfect start when Ozil opened the scoring after four minutes with a lofted left-foot finish which Bournemouth keeper Artur Boruc could not prevent looping in.
And then he showed outstanding awareness to unselfishly square for the in-form Mkhitaryan, who pounced on a sloppy cross-field pass from Bournemouth full-back Adam Smith before playing a one-two with Ozil, to slot in.
Ozil continued to make Arsenal tick throughout and was unlucky not to add another goal himself - when Arsenal led 3-1 - with a low side-footed effort which cannoned back off the post.
"Mesut helped us with his quality and work," Emery said afterwards. "All the players should be proud tonight and it is the same for Mesut."
Ozil's goal was his first since netting in a sublime individual performance against Leicester back in October, before he teed up Mkhitaryan for a first assist in nine league matches.
Whether that was enough to maintain his place against Spurs remains to be seen, but he certainly could not have done more to impress Emery - albeit against a poor Bournemouth side.
Bournemouth have an abysmal record on the road in recent months, having not won an away league game since thumping Fulham at Craven Cottage on 27 October.
The Cherries have lost all nine matches since, with this thumping meaning they have conceded 21 goals in their past six trips alone.
Manager Eddie Howe has been playing down the rotten run, insisting the problem is Bournemouth's general inconsistency rather than a specific mental block when it comes to travelling away.
"Maybe I need to readdress that," Howe said. "We have spoke at length with the players, it is nothing we haven't discussed, but we have to put that into action."
At Arsenal, they were undone by quick goals at the start of each half.
If sloppy defending to go 2-0 down after less than half an hour was bad enough, it got worse when they switched off again after finding a foothold in the game.
Within 90 seconds of the second half restarting, the Cherries defence stood static as Koscielny reacted quickest to convert Mkhitaryan's low cross with the aid of a deflection.
From that point there was no going back - despite Dan Gosling hitting a speculative effort against the crossbar at 3-1 - as they lost nine consecutive away games for the first time since the 1933-34 season.
Despite sliding to 12th position, they remain nine points above the relegation zone with 10 matches remaining - although Howe is refusing to be complacent about their survival.
"We're always looking over shoulder because we need points and we need results," Howe added.
"Whether we are safe or not we need to pride ourselves on being our best and we were way short of that today."
'We imposed our superiority' - post-match reaction
Arsenal manager Unai Emery:
"We worked with intensity and we imposed, little by little over the 90 minutes, our superiority.
"In the first half after we went 2-0 up, they gave us problems. But we showed maturity to continue pushing and doing our work. The second half was good for us.
"It was a good performance and we can be proud of every player."
Bournemouth manager Eddie Howe:
"Arsenal did have individuals who played well and they were too good for us. But that mindset takes away ownership of what we delivered with our own team.
"They may have played well but our perspective is clear that we can do so much better and are capable of much more than that.
"We will not kid ourselves and our analysis has to be that it was not acceptable."
Mkhitaryan looked sharp and was a constant threat against Bournemouth, just like he was three days earlier against Southampton. He became the first Arsenal player to both score and assist a goal in consecutive Premier League appearances since Santi Cazorla in February 2015, being replaced after 64 minutes - with Saturday's trip to Spurs in mind - to a standing ovation
For Arsenal, the short trip to Wembley to face arch-rivals Tottenham. The north London derby kicks off at 12:30 GMT on Saturday.
Bournemouth face another of the top clubs when they host Manchester City at 15:00 on the same day.
