The Blues have only lost once in eight games this season and were coming off a win over fellow New Zealand heavyweights, the Crusaders, which was their first at Christchurch in 18 years.
But they were unsettled by the competition newcomers in their Saturday afternoon clash in Super Round, which features five games over the weekend in Melbourne.
The Blues struggled to find their usual rhythm in the face of the fierce physicality of the Fijians, who have only chalked up one victory in their campaign.
With their silky skills on show the Drua dominated possession but too often were unable to capitalise on the pressure they put on their opponents.
The teams traded early tries for a before the Blues kicked away to a halftime score of 21-10 with two further converted tries.
Lock Sam Darry crossed followed by Marcel Renata, who was on the field while prop Nepo Laulala was in the blood-bin.
League recruit Roger Tuivasa-Sheck was solid in his 60 minute effort, almost setting up a late first-half try before his pass was spilt by his target.
Ten minutes into the second half Blues centre Rieko Ioane showed his acceleration to snatch an intercept and dash 70 metres to touch down but the Drua refused to go away.
They closed to within 10 points when they mauled the ball off a lineout before hulking winger Onisi Ratave busted through the defensive line to touch down.
Blues winger AJ Lam then showed another way to score, using clever footwork to step through for his second of the night, extending their lead to 17 points with 15 minutes remaining.
The Blues had to toil down a man for the final 10 minutes after losing reserve prop Karl Tu'inukuafe to a yellow card after repeated team infringements, but they managed to hang tough to secure a bonus point.
Blues 35 (Tries: Lam 2, Darry, Renata, Ioane, Con: Barrett 5), Fijian Drua 18 (Tries: Dolokoto, Ratave, Con: Kuruvoli, Pen Kuruvoli 2). HT: 21-10.
BLUES: 1. Jordan Lay, 2. Ricky Riccitelli, 3. Nepo Laulala, 4. James Tucker, 5. Sam Darry, 6. Tom Robinson, 7. Adrian Choat, 8. Hoskins Sotutu, 9. Taufa Funaki, 10. Beauden Barrett, 11. AJ Lam, 12. Roger Tuivasa-Sheck, 13. Reiko Ioane, 14. Mark Telea, 15. Jacob Ratumaitavuki-Kneepkens
FIJIAN DRUA: 1. Meli Tuni, 2. Mesulame Dolokoto, 3. Manasa Saulo, 4. Chris Minimbi, 5. Viliame Rarasea, 6. Meli Derenalagi, 7. Rusiate Nasove, 8. Te Ahiwaru Cirikidaveta, 9. Peni Matawalu, 10. Simione Kuruvoli, 11. Onisi Ratave, 12. Caleb Muntz, 13. Kalaveti Ravouvou, 14. Tuidraki Samusamuvodre, 15. Kitione Taliga
RESERVES: 16. Zuriel Togiatama, 17. Timoci Sauvoli, 18. Jone Koroiduadua, 19. Isoa Nasilasila, 20. Joseva Tamani, 21. Leone Nawai, 22. Apisalome Vota, 23. Frank Lomani