De Minaur controlled the match, winning 70 per cent of his service points and converting on four of seven break points en route to the 6-4 6-2 victory.
The Australian fifth seed's return game was also impressive, as usual, as de Minaur won 50 per cent of points receiving serve, while also only committing 18 unforced errors to Tien's 39.
De Minaur broke Tien in the seventh game of the first set following a lung-busting 24-shot rally.
He then closed out the set to love before claiming another break in the opening game of the second set and cruising to victory in 78 minutes.
The world No.10 is chasing valuable points in the race to qualify for the ATP season finale in Turin.
Tenth in the standings before this tournament but needing to be in the top nine because of injury to world No.1 Jannik Sinner, de Minaur's win over Tien provisionally elevates him to ninth in the live rankings ahead of Spain's Rafael Jodar.
De Minaur will next face either No.4 seed Flavio Cobolli or Matteo Berrettini, who clash in an all-Italian affair on Friday (AEDT).
Jodar plays Monaco's Valentin Vacherot for a place in the last 16 at the Swiss Indoors in Basel on Thursday night.
De Minaur's fellow Australian Rinky Hijikata suffered a 6-4 7-6 (7-3) loss to American Taylor Fritz in his first-round clash in Basel.
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