Switzerland and Ukraine took a step closer to reaching the second round of the World Cup on Monday.

Alexander Frei and Tranquillo Barnetta scored a goal each to lead Switzerland to a 2-0 win over Togo, while star striker Andriy Shevchenko got his first World Cup goal in Ukraine's 4-0 win over Saudi Arabia.

Spain played Tunisia later Monday, knowing a win would take it to six points in Group H and guarantee it a place in the second round alongside seven teams already qualified.

Defending champion Brazil, host Germany, Argentina, the Netherlands, England, Portugal and Ecuador are already in the last 16.

With one set of first-round games remaining, Togo was eliminated and Saudi Arabia likely will join it in flying home early.

Frei's performance in Dortmund helped Switzerland to a win that means it only needs 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. He can only improve," Switzerland coach Koebi Kuhn said of Frei.

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Frei gave Switzerland the lead in the 16th minute, heading in a pass from 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 the first half. Togo forward Emmanuel Adebayor looked unlucky not to get a penalty kick when Philippe Senderos brought him down in the penalty area.

"I shouldn't criticize a referee because you get into trouble immediately," Togo coach Otto Pfister said. "You can read and compare to TV. I'm sure you can come to the same conclusion."

In Hamburg, Shevchenko got a header goal and fellow Ukraine striker Serhiy Rebrov scored against Saudi Arabia, which was unable to muster a single shot on goal.

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

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 4-0 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," coach Oleh Blokhin said.