KIEV, Ukraine — The long diagonal pass floated across midfield, its accuracy all the more remarkable for its distance. Waiting with impeccable timing was Mario Balotelli of Italy, one of soccer’s most gifted and eccentric players. He sprinted past the German defense and turned to meet the ball, nimbly switching directions, backpedaling with the gliding agility of a man on skates.

The Germans gave chase, but it was desperate and futile. Already they must have known they would arrive too late. Thirty-five yards from goal, maybe 40, Balotelli let the ball bounce and tap his chest. And he was off again, racing, touching the ball once with his left foot, reaching the edge of the penalty area, the German captain Philipp Lahm in furious and vain pursuit.

Earlier in this semifinal of the European Championships, played Thursday in Warsaw, the 6-foot-2 Balotelli had put Italy ahead, 1-0, with a vaulting header. The narrow stripe of his Mohawk seemed to point to the sweet spot on his forehead as a cross curled in from the flank. The German goalkeeper, Manuel Neuer, moved to his left, but the ball went the other way, beyond his outstretched right hand, and Neuer tossed his water bottle in frustration.

Now Neuer was exposed again, flat-footed, as Balotelli dashed at him. He shot with such power and slicing accuracy that the ball kept rising and swerving until it punched like a fist into the upper right corner of the net. Italy 2, Germany 0. Television cameras caught Joachim Löw, the German coach, picking his fingernails. His team’s chances, probably like his nails, were down to the quick.