The American, who is making his debut in Dallas, had won all three of his previous quarter-finals matches on the ATP Tour heading into his clash against Thompson. And in a dominant display, Brooksby showcased great variety, combining flat groundstrokes with deft slices to ensure his impressive last-eight record remained intact.
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The 21-year-old had not competed at a tour-level tournament since October prior to his victory against Andreas Seppi on Thursday. However, the World No. 54 is playing as if he has never been away, with Brooksby also saving all three break points he faced against Thompson to advance after 73 minutes.
Brooksby now leads the Australian 2-0 in their ATP Head2Head series, having defeated the 27-year-old en route to his maiden tour-level final in Newport in July.