French Open finalist Thiem sprinted out of the blocks in glorious Hamburg sunshine, breaking Millman’s serve twice before serving out the opening set in 33 minutes.
The 24-year-old Austrian carried that momentum throughout the second set, converting a further two break points on his way to a comfortable victory.
Thiem extended his match win record to 38-11 for the season, which includes two claycourt titles in Buenos Aires and Lyon. He will next face Czech Nicolas Jarry for a place in the semi-finals.
Spaniard Pablo Carreno Busta was leading 6-2 4-0 when his opponent Aljaz Bedene was forced to retire due to a hip injury.
Up next for the third seed is Georgia’s Nikoloz Basilashvili, who roared back from 1-6 down in the first set tiebreak to beat 2013 finalist Pablo Cuevas 7-6(6) 6-4.
