With Italy owning a 1-0 lead in the 85th minute, Ibrahimovic picked a bouncing ball out of the air near the Italian goal and flicked it over Christian Vieri to square one of the more entertaining matches of the tournament.
Vieri, a striker, tried to keep the ball out of the net along the goal line while 'keeper Gianluigi Buffon attempted to punch it out of the penalty area.
The Swedish striker's second goal of the tournament spoiled a fine effort by the Italians, who would have moved into first place in the group had they held on.
Denmark, which played a scoreless tie with Italy in its first match, downed Bulgaria, 2-0. The Bulgarians were eliminated from quarterfinal contention.
Any hopes of a comeback were ended when Bulgarian captain Stilian Petrov was sent off at the 83-minute mark after picking up a second yellow card.