There were two rookie coaches hopping around on the touchline and both will feel they have spent a lifetime in management after this emotional rollercoaster. While Frank Lampard seethed at Chelsea’s lack of conviction at both ends of the pitch, Mikel Arteta wondered what on earth he is going to do with Shkodran Mustafi and marvelled at the fearlessness of Gabriel Martinelli. It was that sort of night, absorbing and bonkers in equal measure, and in the end it was difficult to know whether to focus on Chelsea’s sense of bewilderment or Arsenal’s joy.

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For Lampard, the twist was tough to take but easy to explain. Chelsea played for more than an hour against 10 men, led twice and still dropped more points at home. They lacked creativity again, bolstering the argument that they need attacking reinforcements before the transfer window closes, and paid for their carelessness when Martinelli, an 18-year-old winger with a wonderfully direct style, hauled Arsenal level with a stunning solo goal just after the hour.

Chelsea’s imprecision is hurting their push for Champions League qualification – fifth-placed Manchester United will go three points behind them if they beat Burnley at home on Wednesday – and it spoke volumes that they were incapable of holding on after César Azipilicueta restored their lead with six minutes left. Lampard’s side are too loose and Kepa Arrizabalaga’s indifferent form was captured by the moment when Héctor Bellerín, cutting on to his left foot, rescued a point for Arsenal with a shot that somehow squirmed beyond Chelsea’s goalkeeper.

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Arrizabalaga has conceded too many soft goals this season but Arteta was entitled to argue Arsenal merited a draw after a show of defiance in the second half. His side stood up to be counted after Mustafi’s disastrous error led to David Luiz’s red card on 26 minutes. Granit Xhaka excelled as a makeshift centre-half, Martinelli ran Azpilicueta ragged on the left and Arteta, who has lost only one of his seven games, was delighted with his new side’s spirit on a ground where they have suffered in the past.

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Initially David Luiz was the story against his old side. There was no respectful celebration from the Brazilian when he scored here for Paris Saint-Germain in a Champions League tie in 2015 and he looked to make his presence felt from the start, attracting the ire of the Chelsea fans when he charged into the back of Tammy Abraham and kneed the striker up the backside. Battle lines had been drawn.

Abraham would have the last laugh, though David Luiz’s dismissal owed much to the brainlessness of Mustafi. While there have been signs of progress under Arteta, the fact remains the Spaniard has inherited a squad containing a multitude of weaknesses. There is only so much Arteta can improve with his work on the training ground and that was underlined by Mustafi’s blunder.

After a promising opening Chelsea simply had to wait for Arsenal’s most unreliable player to self-destruct. Abraham had fooled Mustafi with a clever turn before scoring his side’s late winner at the Emirates last month and this time he was in the right place when the centre-half sold Bernd Leno horribly short with a staggeringly incompetent back-pass. Abraham raced away, rounded Leno and went down following a desperate lunge from David Luiz.

Facebook Twitter Pinterest David Luiz was shown a red card for his challenge on Tammy Abraham. Jorginho scored the resulting penalty to make it 1-0. Photograph: Elli Birch/IPS/Shutterstock

Stuart Attwell pointed to the spot and how the Chelsea fans chortled when they saw the referee reaching for his red card. David Luiz had denied Abraham a clear goalscoring opportunity and he departed with mocking chants ringing in his ears. All that was left was for Jorginho to tuck his penalty away, giving Chelsea a lead their enterprising football deserved.

Yet Lampard, who hopes to beat Atlético Madrid to the signing of PSG’s Edinson Cavani, would despair at Chelsea’s inability to kill the game. While Callum Hudson-Odoi tested Leno with a rasping drive, they struggled to make the most of their numerical advantage. They lost their shape in midfield, where N’Golo Kanté had a disappointing game, and allowed Arsenal’s belief to grow.

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The hosts flirted with disaster early in the second half, Arrizabalga almost playing Jorginho into trouble. Chelsea’s game management was dismal and Arsenal, who looked blunt at first without the suspended Pierre-Emerick Aubameyang, equalised in the 63rd minute. A Chelsea corner was cleared, Martinelli took possession in his own half, outpaced Emerson, raced clear after a slip from Kanté and slipped the ball past Arrizabalaga.

Lampard turned away in disgust. Chelsea are an infuriating side and they did not convince even after Azpilicueta turned Hudson-Odoi’s cross past Leno. Arsenal fought and Lampard struggled to understand why his players turned down opportunities to put the ball out of play when Abraham went down with an ankle injury. The move progressed, Bellerín drove inside and the Arsenal right-back’s tame shot left Lampard fuming.