Robertson narrowly edged out Murphy in the deciding frame to move into the final of the World Snooker Grand Prix.
The Australian was down 5-3 at one point but fought back, finishing the final frame with his third century break of the match to win the best-of-eleven match 6-5.
The other final spot will be decided later on Saturday evening, when world number one Judd Trump takes on fellow Englishman Stuart Bingham.
The two have previously met 37 times, with Trump winning on 26 occasions.
Robertson narrowly edged out Murphy in the deciding frame to move into the final of the World Snooker Grand Prix.
The Australian was down 5-3 at one point but fought back, finishing the final frame with his third century break of the match to win the best-of-eleven match 6-5.
The other final spot will be decided later on Saturday evening, when world number one Judd Trump takes on fellow Englishman Stuart Bingham.
The two have previously met 37 times, with Trump winning on 26 occasions.
