The 29-year-old, an eight-time national champion in Luxembourg, edged out three-time world road race champion Marianne Vos on the 138.5km stage.
Lizzie Armitstead, one of Majerus' Boels Dolmans team-mates, was the highest-placed Briton, finishing 18th.
Compatriot Rebecca Durrell was 25th, with Olympic gold medallist Dani King one place further back.
1. Christine Majerus (Lux/Boel-Dolmans) 3hrs 24mins 48secs
2. Marianne Vos (Ned/Raboliv) same time
3. Giorgia Bronzini (Ita/Wiggle High5)
4. Marta Bastianelli (Ita/Ale Cipollini)
5. Lotta Lepisto (Fin/Cervelo-Bigla)
6. Leah Kirchmann (Can/Liv-Plantur)
7. Lucinda Brand (Ned/Rabo-Liv)
8. Alison Tetrick (US/Cylance)
9. Elisa Longo Borghini (Ita/Wiggle High5) +6secs
10. Floortje Mackaij (Ned/Liv-Plantur)
Selected others
18. Lizzie Armitstead (GB/Boels-Dolmans) +9secs
25. Rebecca Durrell (GB/Drops)
26. Dani King (GB/Wiggle High5)
34. Grace Garner (GB/British National)
35. Annasley Park (GB/British National)
41. Laura Massey (GB/Drops)
44. Jessie Walker (GB/British National)
Christine Majerus sprinted to victory on the opening stage of the Women's Tour from Southwold to Norwich.