The 10th seed, who is into the third round at the grasscourt Grand Slam for a third straight time, served with consistent precision and won 89% of his first serve points, leaving precious few opportunities for his opponent.
Tiafoe was slightly wasteful in the first set, squandering two break points at 1-0 and a set point at 5-4, as the opener drifted to a tie-break which he eventually claimed.
The second set was more straightforward but it was not all smooth sailing for the American.
He was inches away from being broken in the third set but expertly bailed himself out of a sticky situation by firing off another ace before breaking Stricker at 2-2 with a backhand winner, earning the applause of a limited crowd on Court 12.
Tiafoe will next face the winner of the match between Bulgarian 21st seed Grigor Dimitrov (32) and Ilya Ivashka (29) of Belarus.
