France and Sweden will fight for automatic World Cup qualification next week and the Netherlands needs a miracle just to make it to the European playoffs.
A lone goal from Blaise Matuidi was enough for France to labor past Bulgaria 1-0 in Group A on Saturday, and to secure at least a top-two finish in the race to Russia for the former world champion.
France, which plays its last game against Belarus on Tuesday, kept its one-point lead over Sweden with its first win in Bulgaria since 1932.
The Netherlands is on the verge of elimination despite winning at Belarus 3-1 to stay mathematically in contention, three points behind Sweden, which demolished Luxembourg 8-0.
Sweden travels to the Netherlands on Tuesday enjoying a goal difference of plus-12 over the Dutch.
DUTCH HANGING ON
The Netherlands' narrow victory combined with Sweden's 8-0 thrashing of Luxembourg and France's win in Bulgaria means the Netherlands must beat Sweden by seven goals in Amsterdam on Tuesday to finish second in the group and have a chance of progressing to a playoff.
The score was 1-1 for half an hour until Arjen Robben converted an 84th-minute penalty to break the deadlock. Memphis Depay made the margin look flattering by scoring from an injury-time free kick.
The Netherlands remains at risk of failing to qualify, after finishing third at the 2014 World Cup, and second in 2010.
On a rainy night in Sofia, France needed just three minutes to take the lead. Matuidi was perfectly set up by Antoine Griezmann's short pass in the box and slotted home from a tight angle.
Playing in a 4-3-3 formation with center forward Alexandre Lacazette supported by Kylian Mbappe and Griezmann, France dominated possession and had its fair share of chances.
"It was a complicated and physical game, with a lot of fouls," France coach Didier Deschamps said. "We only had a few chances in the second half, but we did the main thing."
In Solna, Sweden striker Marcus Berg scored four times and captain Andreas Granqvist had a brace in their biggest win in 79 years.
Luxembourg, which held France to a goalless draw last month, endured a nightmarish game.
Sweden scored twice in the opening 18 minutes and led 3-0 at halftime. Incredibly, their second half was even better.