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It was the first time Brazil had lost by two goals since they were beaten 2-0 by Chile in 2015, while they had not conceded four or more in a match since they were humiliated 7-1 by Germany in the 2014 World Cup semifinals.
Harry Kane scored in a 3-0 round-of-16 victory for England against Senegal.
England will meet holders France in the quarterfinals on Saturday.
A draw would have done against Senegal, but Ecuador paid for two lapses in concentration.
Senegal has played in three World Cups including the current one and is one of five African teams taking part in Qatar.
Ecuador need to win or draw to progress but will remain in contention if they lose and Qatar upset the Dutch, who were leading 1-0 at halftime.
They lost 3-1 to Senegal on Friday while the two other teams in its group, Ecuador and Netherlands, drew level and split the points.
Gakpo headed home in the 84th minute to break the deadlock, while Klaassen struck in added time.
The Bayern Munich forward had picked up a leg injury last week.
Group A features hosts Qatar, South American representatives Ecuador, African powerhouses Senegal, and the Netherlands.
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