Arsene Wengers side dominated the game which saw Sime Vrsaljko sent off for the visitors after just nine minutes and Atletico boss Diego Simeone was given his marching orders by the referee moments later.
The visitors owe a huge debt of gratitude to keeper Jan Oblak who expertly denied Alexandre Lacazette and Danny Welbeck in the first-half.
Antoine Griezmann stung the hands of David Ospina late in the first-half after Thomas Parteys powerful run from right-back.
As the Arsenal faithful grew more agitated their team would not find the breakthrough, Lacazette finally got the better of Oblak on the hour with a well-placed downward header following good work from Jack Wilshere.
But when youve got one of the worlds best players lurking, you have to remain alert at all times.
And Arsenal were caught cold when Griezmann latched onto Laurent Koscielnys error before showing great persistence to fire the ball into the net.
Aaron Ramsey nearly won it right at the end with a header but Oblak pulled off another spectacular save as the two sides go into the second leg all square.
It was a very important night for Lacazette, who was in for the cup-tied Pierre-Emerick Aubameyang, but the Frenchman certainly stepped up to the plate.
The striker didnt give the Atletico defence a moments respite and on another night he could have had a hat-trick.
Eventually, Lacazette got his well-deserved goal with an impressive downward header that gave the world-class Oblak no chance.
MOMENT OF THE MATCH
Arsenal were in brilliant form for large periods of the game but they were unable to get the result they needed.
Therefore, the moment of the match has to be the frantic couple of minutes which saw Sime Vrsaljko dismissed and then Simeone was ushered to the stands.
The defender only lasted nine minutes after receiving his second yellow for a nasty challenge on Lacazette before the Atletico boss hostile protests at a foul by Bellerin resulted in him being sent to the stands by referee Clement Turpin, who had a fantastic game.
WHAT THE FANS ARE SAYING
Arsenal XI: Ospina, Bellerin, Koscielny, Mustafi, Monreal, Xhaka, Ramsey, Wilshere, Ozil, Welbeck, Lacazette
Subs not used: Cech, Holding, Iwobi, Chambers, Maitland-Niles, Kolasinac, Nketiah
Atletico Madrid XI: Oblak, Vrsaljko, Gimenez, Godin, Lucas, Thomas, Saul, Correa (Savic 75), Koke, Griezmann (Torres 85), Gameiro (Gabi 64)
Subs not used: Werner, Vitolo, Olabe, Costa
The second leg at the Wanda Metropolitano will be played next Thursday (May 3rd)