The Pacific nation, winners of the Hong Kong Sevens last weekend, booked their place in the last eight by topping Pool A with a 100 per cent record.
Fiji began by thrashing Hong Kong 52-0, before they swept aside Russia 38-7 and Canada 35-7 to complete an ominous start to the tournament at the National Stadium.
New Zealand also progressed with three straight victories as they clinched top spot in Pool D.
The All Blacks Sevens were pushed all the way by Scotland in their group opener as they battled to a narrow 22-21 win.