The two heavyweights were drawn in the same path for the playoffs.
An incident in the goalless draw where Argentine defender Nicolas Otamendi appeared to elbow Raphinha -- which left the Brazilian winger with a bloody mouth -- went unpunished.
Argentina drew goalless with Brazil, while Bolivia boosted their chances with a 3-0 win over Uruguay.
The Netherlands finished with 23 points from 10 games, two more than Turkey, who won 2-1 away to Montenegro to secure a play-off spot.
The Italians were held to a 0-0 draw away to Northern Ireland and must now play in March's play offs.
Portugal, who only needed a draw with Serbia to finish top on goal difference and qualify, will now head into the March play offs.
Holders France ran riot to reach the finals with a match to spare after four goals from Kylian Mbappe helped them to an 8-0 home demolition of Kazakhstan.
The three points take Argentina on to 28 points, six behind Brazil, who on Thursday became the first South American team to guarantee their place in Qatar 2022.
The win extended Brazil’s home run in the qualifiers to 11 consecutive victories, a record in the South American region.
The Danes secured their berth with two games to spare as a 53rd-minute goal from Joakim Maehle helped them to an eighth successive qualifying victory.