Bonzi broke for 3-1 to dominate the opening set 6-3 in 29 minutes, with Norrie unable to mount sustained pressure.
Norrie broke for 5-3 after saving a break point in a 5 minute hold for 4-3, then held for 6-3 to level despite Bonzi saving two of three break points in an 8 minute game.
Bonzi broke for 2-0 and again for 5-3, sealing 6-3 with a deuce hold for 6-3 saving one break point, while Norrie's sole resistance came from a 6 minute deuce hold for 1-3 saving both break points.