Mikel Arteta’s side lost control of the title race after last week’s 4-1 defeat at Manchester City.
But the Gunners signalled their intention to push City all the way to the wire with a much-needed first win in five games.
Odegaard’s brace was followed by a Gabriel Jesus strike as the hosts raced into a three-goal before half-time at the Emirates Stadium.
Noni Madueke’s second half goal was no consolation for Chelsea’s wretched performance.
Arsenal are now two points clear of second placed City and while Pep Guardiola’s men remain favourites to win the title, the north Londoners have at least applied a little pressure on the champions.
City will go back into first place if they beat West Ham at home on Wednesday in the first of their two games in hand on Arsenal.
After 10 weeks at the top, Arsenal were knocked down to second place by City’s win at Fulham on Sunday.
Three successive draws, including two blown two-goal leads, and the calamitous loss at City have led Arsenal to be written off as title race chokers.
But Arteta insisted this week that the title was still winnable and his players responded to the Spaniard’s rallying cry.
Troubled Chelsea were ideal opponents for Arsenal to get back on track before a tricky trip to Newcastle on Sunday.
The Blues have now lost all six games since Frank Lampard returned as caretaker boss to replace the sacked Graham Potter.
Languishing in 12th place, Chelsea are on an nine-game winless run in all competitions and face the prospect of failing to finish in the top half of the table for the first time since 1996.
Former Arsenal forward Pierre-Emerick Aubameyang made his first Chelsea start since the Blues lost 1-0 to the Gunners in November.
But Aubameyang, whose four-year spell with Arsenal ended acrimoniously in 2022, never had a chance of exacting revenge on his old team before being hauled off at half-time.
Foreshadowing Chelsea’s implosion, Cesar Azpilicueta gifted Arsenal a golden opportunity in the opening moments when his woeful header was intercepted by Granit Xhaka, whose close-range effort was saved by Kepa Arrizabalaga.
Arsenal were in complete control and Odegaard gave them a deserved lead in the 18th minute.
Left in acres of space, Xhaka’s low cross eluded Chelsea’s lackadaisical defenders and Odegaard guided a superb curling finish past Kepa from just inside the penalty area.
Ben Chilwell threatened a Chelsea equaliser against the run of play when the left-back’s run behind Bukayo Saka gave him a clear sight of goal, but Aaron Ramsdale made a fine save to preserve the lead.
That near-miss was a false dawn for abysmal Chelsea as the Gunners turned the screw with a second goal in the 31st minute.
Once again, Chelsea allowed Xhaka time to cross into the area and Odegaard took full advantage of slack marking from Raheem Sterling to fire past Kepa from 12 yards.
Arsenal scented blood against spineless, disinterested opponents and the third goal duly arrived three minutes later.
Ben White’s cross was chested down by Jesus and when Xhaka’s shot was blocked, it was Jesus who stabbed home from close-range.
Arsenal were rampant and Thiago Silva hooked Gabriel’s header off the line, while Kepa made yet another save from Xhaka.
Saka was denied by Kepa’s out-stretched leg before Chelsea awoke from their slumber just long enough to reduce the deficit in the 65th minute.
Mateo Kovacic’s defence-splitting pass found Madueke and he deftly slotted past Ramsdale for his first league goal since signing from PSV Eindhoven in January.
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