Italy will meet Germany in the World Cup semi-finals as they beat Ukraine to extend their unbeaten run to 23 games.
Toni gets on the scoresheet for the World Cup for the first time
Ukraine adopted a policy of containment but were behind after six minutes when keeper Olexandr Shovkovskiy was unable to keep out Gianluca Zambrotta's shot.
Italy extended their lead when Luca Toni guided home a 59th minute header.
Maxim Kalinichenko twice hit the woodwork for Ukraine either side of Italy's second, before Toni sealed the win as he converted Zambrotta's cross.
Italy were well worth their win, with Gianluigi Buffon superb in goal.
Ukraine's hopes of saving the game were scuppered by Buffon's heroics as he saved from Kalinichenko and Gusev early in the second half.
Ukraine's cause was not helped by the anonymity of Andriy Shevchenko, who for long periods was reduced to a virtual spectator by the close attentions of the Italian defence.
Ukraine's defence proved less disclipined.
Just before Zambrotta's goal Mauro Camoranesi had gone close with a run and a shot as the Ukraine defence backed off.
Ukraine failed to learn the lesson of allowing Italy to run at them and Zambrotta punished their laxness.
Shovkovskiy got his hands to Zambrotta's shot, but it was too powerful for him as the ball flew into the corner of the net.
Francesco Totti's exquisite back-heel released Zambrotta into the space he exploited so zealously for his goal and throughout the Roma playmaker's vision and touch illuminated the game.
Shevchenko had a subdued game for Ukraine
Totti also provided the cross for Italy's second goal as Toni shook off the attentions of Andriy Gusin before stooping to head past Shovkoskiy.
Italy's buoyant start prompted an immediate tactical switch from Ukraine as coach Oleg Blokhin threw on Andriy Vorobey in place of Viacheslav Sviderskiy, who had been man-marking Francesco Totti.
But Ukraine still struggled to threaten Buffon in those opening 45 minutes, their best efforts a misdirected Shevchenko header and an Anatoliy Tymoschuk shot.
In first-half stoppage time Ukraine had to make a second substitution when the injured Andriy Rusol limped off and was replaced by Vladislav Vashchuk.
Ukraine were more positive after the restart and Kalinchenko's downward header hit the post as Buffon pushed the ball on to the woodwork.
Fabio Cannavaro proved just as alert when he brilliantly headed clear Vorobey's cross from the right.
Immediately after Toni's first goal, Ukraine struck the woodwork for a second time when Kalinchenko rose above Fabio Grosso to thump a header against the bar.
Ukraine's slim hopes of causing an upset disappeared when Zambrotta's cross presented Toni with the easiest of chances to claim his second goal of the tournament.
Italy: Buffon, Zambrotta, Cannavaro, Barzagli, Grosso, Perrotta, Pirlo (Barone 68), Gattuso (Zaccardo 76), Camoranesi (Oddo 68), Toni, Totti.
Subs Not Used: Amelia, Del Piero, Gilardino, Iaquinta, Inzaghi, Nesta, Peruzzi.
Goals: Zambrotta 6, Toni 59, 69.
Ukraine: Shovkovskiy, Nesmachniy, Sviderskiy (Vorobey 20), Rusol (Vashchuk 45), Tymoschuk, Shelayev, Gusev, Gusin, Kalinichenko, Milevskiy (Byelik 72), Shevchenko.
Subs Not Used: Nazarenko, Pyatov, Rebrov, Rotan, Shust, Voronin, Yatsenko, Yezerskiy.
Booked: Sviderskiy, Kalinichenko, Milevskiy.
Ref: Frank De Bleeckere (Belgium).
Fifa man of the match: Gennaro Gattuso
This 3-0 triumph equals Italy's second biggest winning margin ever at the World Cup. The 7-1 victory against the United States in 1934 remains their most comprehensive World Cup success.
Italy have reached the semi-final knock-out stage of the World Cup for the seventh time, and the first time since 1994. They also reached this stage in 1934, 1938, 1970, 1982 and 1990. They qualified for the last four in 1978, but never went through a knockout phase as they advanced from a semi-final group stage. Opponents have still not scored a goal against Italy at this tournament. The only goal the Italians have conceded so far was an own goal by Cristian Zaccardo in the match against United States (1-1).
Ukraine have been the best debutants at the 2006 World Cup as they reached the quarter-finals.
Trivia stats source: Infostrada Sports