William Owen, 45, of Nefyn, Gwynedd, admitted speeding on the 60mph A499 near Pwllheli in March.
Caernarfon Magistrates' Court chairman Alwyn Lloyd Ellis said it was "unbelievable speed in the middle of the day".
Owen was fined Â£500 with Â£135 costs and banned from driving for six months.
The prosecution said the police officer paced the Volkswagen Golf at a "safe but constant" distance behind.
Michael Strain, defending, said the vehicle coming up behind him had "spooked" Owen.
A driver who sped at 122mph to get away from someone he thought was tailgating him did not realise it was an unmarked police car, a court heard.