BERLIN -- Spain may be about to shake off its tag as World Cup underachiever.

A perennial disappointment in the tournament, Spain trailed Tunisia for much of Monday's game before scoring three late goals for a 3-1 win and a place in the second round.

Switzerland and Ukraine each won to move a step closer to qualifying from their first-round groups. Switzerland beat Togo 2-0, while Ukraine trounced Saudi Arabia 4-0.

Spain trailed in Stuttgart after an eighth-minute goal by Tunisia's Jahwar Menari and appeared set for a surprising loss before a 71st-minute equalizer by Raul Gonzalez and two goals from Fernando Torres.

For his first, Torres collected a pass at the halfway line, took two quick touches and flicked the ball past the goalkeeper with the outside of his right boot from the edge of the penalty area.

His second goal was a 90th-minute penalty kick awarded when a defender held Torres to stop him from jumping for a header. That goal made him the tournament's leading scorer with three.

Having beaten Ukraine 4-0 in its opener, Spain has six points in Group H and is the eighth team to reach the second round. Its best World Cup showing was a fourth-place finish in 1950.

Defending champion Brazil, host Germany, Argentina, the Netherlands, England, Portugal and Ecuador are already into the last 16. Tunisia must beat Ukraine on Friday in its last game to have a chance to advance.

Togo was eliminated and Saudi Arabia looks likely to join the African team.

Alexander Frei's performance in Dortmund helped Switzerland to a win that means it needs only a draw against South Korea in its last Group G game to guarantee a spot in the second round.

"We all know he can be even more efficient than we saw today, but he's coming back from a long injury period," Switzerland coach Koebi Kuhn said. "He can only improve."

Frei gave Switzerland the lead in the 16th minute, heading in a pass from Tranquillo Barnetta. Frei missed a chance to score in front of an open net early in the second half, but Barnetta added another in the 88th with a 17-yard shot.

In Hamburg, Andriy Shevchenko got a header and Serhiy Rebrov scored one of the best goals of the tournament in Ukraine's win against Saudi Arabia, which was unable to muster a single shot on goal.

Andriy Rusol had already scored from a corner, the ball bouncing off his knee and into the goal, then Rebrov hit a 35-yard shot into the right-hand corner of the net in the 36th minute.

Shevchenko made it 3-0 in the 46th and, with four minutes remaining, set up Maxim Kalinichenko for the final goal that completed a turnaround from the team's opening loss to Spain.

"I think our chances of going all the way are not huge because there are stronger teams, but we will fight," Ukraine coach Oleh Blokhin said.