Australian No.1 Alex de Minaur has marched into the second round of the ATP 500 event in Rotterdam but compatriot John Millman was an early casualty in Dallas.

Alex de Minaur has dropped just three games against former world No.7 David Goffin to storm into the second round of the World Tennis Tournament in Rotterdam.

The Australian No.1 dominated proceedings for most of the match and despite a small hiccup closed out a comprehensive 6-0 6-3 victory in one hour and 15 minutes.

De Minaur, coming off his best performance at his home grand slam last month when he reached the fourth round at the Australian Open, was impeccable in the opening set against Goffin and took just 29 minutes to wrap it up.

While Goffin broke de Minaur's serve to take a 2-1 lead in the second set that was as good as it got for the Belgian.

De Minaur immediately broke serve to love and did so again in the eighth game before he sealed the win on his first match point.

"I think I played really well," de Minaur said on the ATP Tour website.

"I played exactly how I wanted to."

De Minaur is now 3-0 in career meetings against Goffin, who has slipped down the rankings to 47th.

"My coach and I set up a plan about how we wanted to play this match and I managed to execute it. It is a very good feeling," de Minaur said.

"Mentally I thought I was very solid and positive and that is one of the main aspects I am trying to focus on this year."

Next up for world No.34 de Minaur is a meeting with American Mackenzie McDonald, who accounted for eighth-seeded Nikoloz Basilashvili 6-3 6-2 in the opening match of the main draw.

Polish fourth seed Hubert Hurkacz defeated French wildcard Jo-Wilfried Tsonga 6-4 7-6 (9-7) in their opening round encounter.

Meanwhile, John Millman went down to Brandon Nakashima in a tight two-set battle in the opening round of the inaugural Dallas Open.

The 20-year-old American beat the experienced Australian 7-5 7-6 (7-3).

Millman was up a break of serve in the second set but was unable to extend the match as Nakashima won the final four points to seal the result.

with AP