The Australian has been troubled by injuries in 2014, but appears to be getting back to his best on the evidence of his 7-6 (7-4) 6-4 victory over South Africa's Anderson in the ATP 250 hard-court event.
Tomic produced an impressive performance against the world number 17 Anderson, who failed to secure a solitary break of serve and has now lost all three of his matches against the 21-year-old on the ATP Tour.
The first set went with serve after Tomic fended off three break points, and then claimed four points on Anderson's serve in the tie-break to take the upper hand.
Anderson then slipped up in the third game of the second set, as Tomic claimed the decisive break to set up a clash with seventh seed Fernando Verdasco in the last eight.
Grigor Dimitrov began the defence of his title with a 7-5 7-6 (7-4) victory over Russian Teymuraz Gabashvili.
The second seed from Bulgaria clinically converted four out of five break points en route to the last eight and will now face either Jack Sock or Jeremy Chardy.
There was a sense of deja vu for Verdasco, as he beat Finland's Jarkko Nieminen for the second successive year in the second round.
The Spaniard won 7-6 (7-4) 6-4 to reach the quarter-finals in Sweden for a third time and thwart Nieminen once again.
American Sock is on the rise having reached a career-high ranking of 51, and he showed why by sending down 11 aces in a 6-1 4-6 6-1 first-round win over Kazakhstan's Andrey Golubev.
Qualifiers Dustin Brown and Pierre-Hugues Herbert advanced to the second round by beating Christian Lindell and Pablo Carreno Busta respectively.
Germany's Brown downed local wildcard Lindell 6-4 7-6 (7-3), while Frenchman Herbert edged out Spain's Carreno Busta 7-6 (7-3) 6-4.