Ralf Rangnick's side crashed out after Anthony Elanga blazed his spot-kick over the bar in a nerve-jangling shoot-out. Swedish teenager Elanga was the only player from either team to miss in the shoot-out, leaving the forward holding his head in disbelief as Middlesbrough celebrated their stunning victory.
Jadon Sancho had put United ahead in the first half, but Matt Crooks grabbed a controversial equaliser after the interval to set the stage for Middlesbrough's memorable upset. Crooks' goal was allowed to stand despite Duncan Watmore controlling the ball with his hand before providing the assist.
Cristiano Ronaldo had missed a first half spot-kick for United, who have now lost seven of their last eight penalty shoot-outs, including last season's Europa League final against Villarreal.