Viktor Gyökeres' first-half penalty gave Arsenal the lead but Atleti and Julián Alvarez had the answers in an absorbing encounter in Madrid.
Key moments
14' Alvarez forces sharp Raya save
44' Gyökeres powers in penalty
49' Alvarez close with curling free-kick
53' Lookman denied, Griezmann shot blocked
56' Alvarez equalises with perfect penalty
63' Griezmann hits woodwork
74' Lookman denied by Raya
90+4' Molina fizzes over
Match in brief: Atleti hit back against Arsenal
A string of half-chances marked out a tight first-half contest before Viktor Gyökeres' clinical penalty sparked this semi-final first leg into life.
As it happened: Atleti 1-1 Arsenal
Piero Hincapié, Martin Ødegaard and Noni Madueke had come close for the Gunners while Atleti's Julián Alvarez stung the palms of David Raya after some artful footwork in the 14th minute and later headed over from Matteo Ruggeri's delivery.
A first-half breakthrough seemed unlikely as chances came and went but Gyökeres had other ideas, the Swedish forward dispatching powerfully from the spot on 44 minutes having been brought down by Dávid Hancko.
Atleti were level within 11 minutes of the restart, Alvarez, Ademola Lookman and Antoine Griezmann threatening as part of an electric start before the Argentinian forward ripped a perfect penalty into the top-left corner following a Ben White handball.
Diego Simeone's charges remained on top, Griezmann striking the crossbar and Lookman testing Raya in the ensuing 20 minutes, and enjoyed the best opportunity of the closing stages too – Nahuel Molina firing over in stoppage time.
Starting line-ups
Atleti: Oblak; Llorente, Pubill, Hancko, Ruggeri; Simeone (Le Normand 46), Koke, Cardoso (Molina 88), Lookman; Griezmann, Alvarez (Álex Baena 77)
Arsenal: Raya; White (Mosquera 86), Saliba, Gabriel, Hincapié; Ødegaard (Eze 57), Zubimendi, Rice; Madueke (Saka 68), Gyökeres (Jesus 68), Martinelli (Trossard 68)
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What's next?
The second leg takes place in London on Tuesday 5 May.
The aggregate winners will face Paris or Bayern in the final at the Puskás Aréna, Budapest, on Saturday 30 May.