Anderson conceded four break point chances in the opening set, and Tomic pounced on the one he needed to wrap up the set, much to the pleasure of the Sydney crowd.
But the powerful South African was on song on his own delivery in the second set, winning all bar two of his points on serve, including all 21 behind his first ball to win it in a tie-breaker.
However, the big-serving Anderson caved to Tomic's pressure in the decider, double-faulting to hand the Australian a 5-3 lead, and the local hope was able to serve it out in style.
Tomic won 16 of 18 points on his first serve in the final set and it proved a decisive serving performance.
He has enjoyed almost ideal preparation for the season-opening grand slam after shocking world number one Novak Djokovic at the Hopman Cup in Perth, before beating countryman Marinko Matosevic (47), Florian Mayer (26) and Andreas Seppi (22) this week.
