The county's team is now one of eight World Cup qualifying European group runners-up set to meet in play-offs in November, after securing second place above the Dutch in Group A on goal difference.
Arjen Robben scored both first-half goals for Holland, who fell short of the seven-goal margin needed to replace Sweden in the play-offs for a place in the World Cup in Russia.
The 33-year-old announced his international retirement after the match, which petered out in the second half as Sweden 'shut up shop', packing out their defence and making no effort to go forward.
The two teams finished level on 19 points, behind group winners France, who secured top spot and automatic qualification after a 2-1 win at home to Belarus.
Sweden now await Tuesday's draw for the play-offs. As one of four unseeded teams in the draw, they will face either Switzerland, Italy, Croatia or neighbours Denmark.
There is no doubt which team the Swedes want to avoid in next week's draw.
"Not Italy," said defender Andreas Granqvist when asked what country he wished to face.
"It will be fun. It will be excited. We are not seeded but we have shown that we can beat anyone, so we will see who we get," Granqvist said.
"For me, Italy is maybe the strongest team, they have a really great defence. Croatia have fantastic players but have maybe had a few problems," the striker said.
"I think we have a chance against anyone. Denmark and Switzerland are two interesting teams who we maybe have the biggest chance against," added Berg, who scored four goals in Sweden's 8-0 victory over Luxembourg on Saturday.
"I have not thought so much about it. There are very good teams in the play-offs, so there's no point speculating, we'll wait and see who we get. It is goalless at the start and then we have 180 minutes to see who will go to the World Cup," the Hull City midfielder said.
The first legs will be played on 9-11 November, with the second legs on 12-14 November.