Having been dragged into a five-set battle in his opener and forced to negotiate two tiebreaks in the next, the Italian looked increasingly at home on the grass of Court One and gave Brooksby very few opportunities to disrupt his rhythm.
The 24-year-old got down to business with little interest in another energy-sapping encounter on a warm afternoon, grabbing a break for a 4-3 lead after Brooksby sent his forehand long, and then motoring through the opening set in only 37 minutes.
World number 81 Brooksby looked to mix it up and drew Sinner to the net more in the next set, but there would be no payoff as the four-times Grand Slam champion countered it with his superb movement and swiftly doubled his lead in the match.
A blistering backhand winner helped Brooksby break first in the next set but top seed Sinner responded immediately and held his nerve after dropping serve late on for a last 16 meeting with Japanese qualifier Shintaro Mochizuki.