The 28-year-old skated in the fifth of 12 heats, well before the favourites, but her dazzling time of 3:59.21 held up to win.
Ireen Wust, the 2006 and 2014 champion, was a narrow second in 3:59.29 with Antoinette de Jong third in 4:00.02.
Achtereekte was third at the Dutch Olympic trials and second in last month's European championships in 4:06.81, but was a shock winner when it matter most.
Wust took her ninth Olympic speed skating medal, matching the all-time record total of Germany's Claudia Pechstein and tying the Dutch career record for Olympic medals by equestrian rider Anky Van Grunsven.
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Wust missed out on becoming the first Dutch woman to defend a Winter Olympic title and only the second woman with back-to-back golds in the event.
Wust also narrowly failed to become the first Dutch athlete to win five Olympic golds in the Winter or Summer Games.
Czech Martina Sablikova, the 2010 Olympic champion and silver medallist at Sochi, was fourth, just 0.52 behind de Jong, with Japan's Miho Takagi fifth in 4:01.35.
Pechstein, a record nine-time Olympic speedskating medallist who turns 46 later this month, missed her chance to win a medal at a sixth different Winter Olympics, finishing ninth in 4:04.49.