Spain's 4-0 thrashing of Ukraine last week gave Luis Aragones's side control of the group. A second win over Tunisia in Stuttgart will secure their place in the last 16.
Ukraine, stinging from the rout, have to wipe it from their minds before taking on Saudi Arabia in Hamburg.
Despite the heavy defeat in their debut appearance in the finals, Oleg Blokhin's team should still qualify.
Striker Andriy Shevchenko, back after a knee injury, looked out of sorts against Spain. Even if he remains off the pace, Ukraine can expect to beat the Asian qualifiers.
Saudi Arabia allowed Tunisia to grab a last-gasp 2-2 draw last week and consider the Ukraine encounter decisive for their chances of progressing, with Spain still to come.
Spain striker Fernando Torres urged his team to keep their feet on the ground, despite stretching their run to 23 matches without defeat.
"We've done nothing so far, we've just played one good game," said striker Fernando Torres.
SLIM HOPES
Tunisia's slim homes of claiming a second World Cup win in 11 attempts spanning four World Cups have been hit by striker Francileudo Dos Santos's failure to recover from a shin injury that also ruled him out of their opening match.
The top two in Group H face their counterparts from Group G in the second round and Switzerland can take a step towards securing first place, probably avoiding Spain, by beating Togo in Monday's other game.
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Togo should be well briefed by their German coach Otto Pfister, who is married to a Swiss, lives in Switzerland and played and coached in the country.
The Africans have now settled the pay row among their squad, a dispute that caused Pfister to resign briefly before he returned to oversee the 2-1 defeat by South Korea.
A win for Switzerland would put them on four points alongside Korea after the 2002 semi-finalists snatched a 1-1 draw with France in Sunday's late match.
Elsewhere, Brazil eased into the second round with a 2-0 victory over Australia thanks to goals from Adriano and Fred while Croatia and Japan shared a 0-0 draw.