The Melbourne cueman won 5-3 against Jamie Cope to seal a spot against either Joe Perry or Stuart Bingham in the last eight.
Cope opened with a 74 break to take the lead but Robertson levelled with an 82 run then moved ahead.
Cope drew level only to fall two frames behind as the Thunder from Down Under compiled breaks of 83 and 91.
Cope edged a scrappy seventh frame to stay in the match, but the reprieve was short-lived as a 68 from Robertson finished the job.
Neil Robertson 5-3 Jamie Cope
Dominic Dale 5-2 Fergal O’Brien
Robert Milkins 5-3 Ben Woollaston
Mark Davis 5-4 Paul Davison
Marco Fu 5-2 Ken Doherty