Former world champion Robertson, who has enjoyed a perfect start to the season, secured the Wuxi Classic title in China last week and is making inroads to get his hands on the trophy in Australia.
Robertson lost the opening frame, but hit back with two quick frames of his own - a break of 65 in the third allowing for the Australian to take the lead for the first time in the match.
Milkins hit back shortly after, but was powerless to stop Robertson from claiming the next three to wrap up the match.
Robert beat me at the World Championship last year so I know how good he is," said Robertson.
"I didn't score heavily enough when I had the chances so 5-2 was a bit flattering because it could easily have gone 3-3. I didn't play as well as yesterday. The table was really nice to play on but it was a bit too quick off the cushions and I lost position a couple of times because of that.
"The most important thing is to win - it's really pleasing when you play your best, but you can't do that all the time. I'm really proud to be into the weekend stage here."
Mark Davis 5 - 4 Stuart Bingham
Neil Robertson 5 - 2 Robert Milkins
Xiao Guodong 5 - 2 Matthew Stevens
Judd Trump 5 - 4 Ricky Walden