The British No1 followed up hard-fought wins over Holge Rune and compatriot Andy Murray at the Western and Southern Open by brushing aside American teenager Ben Shelton.
Norrie produced an emphatic bagel in the first set before swiftly wrapping up the second 6-2, sealing the most comfortable of victories inside just 58 minutes.
Next up for the 26-year-old is a far trickier showdown with Spanish sensation Carlos Alcaraz, who saw off Marin Cilic in round three after an opening victory over Mackenzie McDonald.
Norrie has lost all three of his previous ATP Tour meetings with Alcaraz, 19, including a straight-sets loss in the first round at last year’s US Open.
Alcaraz ended Norrie’s Indian Wells title defence at the quarter-final stage in March and also knocked him out of the Madrid Open in May.
The Spaniard is currently ranked fourth in the world, but could move up to second behind Daniil Medvedev by winning the tournament in Cincinnati, leapfrogging Rafael Nadal and Alexander Zverev.