Australian Robertson won the Masters two months ago and is closing in on the £70,000 top prize at the Bailey Allen Hall, with Stephen Maguire awaiting him in the last four.
A run of 131 that equalled Ricky Walden's highest break of the tournament gave Robertson the first frame of the contest.
Perry then levelled at 1-1 with a break of 100 which was helped by a fluke on the penultimate red.
Robertson claimed a scrappy third frame before a long pot on the last red proved crucial in helping him take the fourth before he sealed the win in the next with a run of 52.
"I felt fantastic tonight and if I hadn't missed three easy balls I could have had more centuries," Robertson told worldsnooker.com.
"I wasn't sure how I would feel because Joe and I are such good friends. He had chances in the third and fourth frames and if he had taken them it would have been different.
"My attitude to the PTCs this season was a lot better, I embraced them and played in as many events as I could. It's good prize money here and now I'm getting the rewards."
Scot Maguire continued his fine run of form as he edged past Walden 4-3, while the other semi-final will see Andrew Higginson - who beat surprise packgae Xiao Guodong 4-1 - take on another man in form, Stephen Lee who showed his intent with a 4-0 whitewash of world No 1 Mark Selby.