The Spain striker fired Atletico in front inside a minute, had completed his hat-trick by half-time as the Rojiblancos led 5-0, added another after the break and was sent off in a lively clash which was almost entirely dominated by Diego Simeone’s side.
Costa was set up in the box by the excellent Joao Felix after just 45 seconds and the striker’s shot deflected in off Sergio Ramos to give Atleti a dream start.
If there was an element of luck about that one, Atletico soon showed they were in complete control as Saul crossed from the left and Joao Felix slotted in for 2-0 with just eight minutes on the clock.
Angel Correa, who had replaced the injured Alvaro Morata minutes earlier, turned and instinctively steered the ball into the corner for a third after good work by Koke.
That was after 19 minutes and Madrid were shell-shocked. Things soon got worse for Zinedine Zidane’s side too as Saul intercepted a loose pass by Ramos to Luka Modric and quickly freed Costa for a simple finish past Courtois after 28 minutes.
Vinicius Junior then hit the post late in the first half as Madrid finally awoke, but Isco clattered Costa in the box at the end of the opening period and the striker piocked himself up to fire in a cool penalty for 5-0 at the interval.
Five soon became six as Costa bagged his fourth after 51 minutes, the Brazil-born forward collecting a super pass from Joao Felix and chipping beautifully over the advancing Keylor Navas.
Madrid then pulled a goal back after an hour as Nacho bundled in from close range following excellent play on the byline by the otherwise-quiet Eden Hazard.
And just a few minutes after that, Costa and Dani Carvajal were both sent off, having committed a cynical foul apiece and then squared up in ugly scenes at the MetLife Stadium.
Vitolo came off the bench and ran through the heart of the Madrid defence before firing in a low shot from just inside the box for 7-1 with 20 minutes still left and the attacking midfielder almost scored again moments later.
Both sides had made a sea of changes by then and Gareth Bale was on for what may well be his last appearance before moving to China. The Welshman had a couple of efforts late in the game, but could do little to affect the proceedings at that point.
Madrid did pull two goals back, though, substitute Karim Benzema netting from the spot after Nacho was fouled by Hector Herrera and youngster Javi Hernandez poking home from close range right at the end.
The final whistle went soon after that and if anything, the 7-3 scoreline did not tell the whole story of Atleti’s complete control in this match. Madrid, meanwhile, were poor again and Los Blancos have now conceded 12 goals in their three pre-season games so far this summer.