Mead grabbed a try and ran for 139 metres as he led his country to their eighth win in their past 11 Test matches.
Fiji looked to have struck the first blow in the 10th minute when Taane Milne powered crashed over from close range but he was ruled to have lost the ball on the way to the ground.
Not to be denied the Bati kept the pressure on and co-captain Kevin Naiqama opened the scoring when he put in a grubber and cleaned up the scraps after Dan Russell had fumbled the ball.
