Replacement Atletico goalkeeper Antonio Adan was the hero on his debut in the International Champions Cup contest, saving three penalties before scoring the winning spot kick himself to get his side's pre-season preparations off to a winning start.
Atletico had taken the lead shortly before half time when Luciano Vietto opened the scoring against the run of play, but Arsenal responded in the opening stages of the second half through promising youngster Emile Smith Rowe's memorable strike.
However, the Gunners scored just one of their four penalties as their youthful side went down to an Atletico team missing the majority of their star players due to World Cup duties.
Emery included summer signings Matteo Guendouzi and Bernd Leno in his starting lineup, but the latter did not have much to do during his 45 minutes on the pitch aside from picking the ball out of the back of his net as Arsenal dominated possession against their depleted opponents.
Reiss Nelson's pace caused Atletico early problems, with one run taking the Arsenal youngster to the byline before he stood the ball up to the back post for Pierre-Emerick Aubameyang, whose volley was deflected behind by Juanfran.
Aubameyang had an almost-identical chance to his first effort when he peeled away from his marker to meet a corner, but once again he failed to connect properly with his first-time volley and sent it bouncing wide of the target.
The first shot on target did not arrive until midway through the first half when Alexandre Lacazette battled to win the ball back inside the Atletico area, but the angle was against him and Jan Oblak was not fooled by his attempts to sneak it in at the near post.
Atletico did begin to grow into the game as the first half wore on, with Rodri and Thomas Partey both miscuing efforts, and the Spanish outfit created their first clear chance of the match shortly before the half-hour mark.
Vietto then fired a half-volley over the crossbar before Arsenal responded with a chance of their own when Ramsey flicked a clever ball around the corner to release Lacazette, who was once again denied by Oblak from a tight angle.
The Gunners should have opened the scoring in the 39th minute when Smith Rowe fed the ball into the path of Lacazette, whose low strike was parried by Oblak into the path of Nelson. The Arsenal youngster had the goal gaping, but Roberto Olabe's last-ditch challenge was enough to put Nelson off and he blazed his finish over the crossbar.
It proved to be a costly miss, too, as Atletico took the lead against the run of play with their first shot on target just two minutes later. Correa's whipped cross was met with a powerful header by Vietto, who sent the ball flying past a helpless Leno and into the top corner.
A Rob Holding header which drifted wide was all Arsenal could muster in response during the closing stages of the first half, but they were level within two minutes of the restart when Smith Rowe announced himself with a stunning equaliser.
The 17-year-old created space to shoot from 25 yards out and curled his subsequent effort into the top corner past Adan, who was beaten just a couple of minutes into his debut after coming on at half time.
Arsenal continued to dominate in the opening 10 minutes of the second half with Ramsey, and Aubameyang both having long-range efforts, but Atletico soon responded and somehow failed to take the lead shortly before the hour mark.
A couple of defensive errors from Arsenal gifted Diego Simeone's side two glorious chances within seconds of each other, but Petr Cech pulled off a brilliant reaction save to deny the first before a last-ditch block sent the second behind for a corner.
Rodri was left unmarked from the subsequent delivery only to nod his effort over the crossbar, and Arsenal survived two or three more scares in quick succession as Atletico kept the pressure on.
However, wholesale changes from both managers during the second half upset the rhythm of the match, and the closest either came to preventing a penalty shootout after the hour mark was when Eddie Nketiah was denied by Adan eight minutes from time.
With so many youngsters on the pitch it was perhaps no surprise that the shootout lacked a certain degree of quality, with Correa setting the tone when he hit the post with the opening spot kick.
Ainsley Maitland-Niles finally got Arsenal off the mark with a Panenka dink down the middle, but Nketiah was also denied by Adan and the Atletico keeper then took on the match-winning responsibilities himself, firing the best penalty of the shootout in off the bar to wrap up the victory.
Arsenal will next face Paris Saint-Germain in Singapore on Saturday, before Atletico also take on the French champions in their second ICC outing two days later.
ARSENAL (4-2-3-1): Leno (Cech 46'); Bellerin (Mavropanos 63'), Mustafi (Chambers 63'), Holding (Sokratis 63'), Kolasinac; Ramsey (Osei-Tutu 63'), Guendouzi (Willock 74'), Nelson (Mkhitaryan 63'), Smith Rowe (Maitland-Niles 63'), Aubameyang (Perez 63'); Lacazette (Nketiah 63')
ATLETICO (4-4-2): Oblak (Adan 46'); Juanfran (Munoz 74'), Moya (T Rodriguez 74'), Rubio (P Rodriguez 74'), Olabe (Solano 74'); Correa, Rodri, Partey (Carro 74'), Joaquin (Pinchi 64'); Gameiro (Mollejo 74'), Vietto (Garces 74')