The Australian has been in scintillating form all week in Glasgow and continued it with four frame-winning breaks to start the match.
A century in the first frame was bettered by a 135 clearance in the fourth as the left-hander set Higgins a mountain to climb.
To his credit, the home favourite emerged from the interval to halve the deficit, a 68 break in frame six reducing Robertson's lead to 4-2, and added a third frame to get within one at 4-3.
Robertson was unmoved, however, and dominated the eighth frame. A half-century promised more before he ran out of position, but a long-range miss from Higgins allowed Robertson back to the table where he quickly restored a two-frame lead to move within one of the final.
Higgins looked set to stay alive by taking the ninth but a missed black off the spot allowed Robertson back to the table, and he made no mistake.
"You've got to enjoy the pressure and nerves," said Robertson, now down at 20th in the world but sure to rapidly climb the rankings in this form.
"Second final of the season, if I win tomorrow all of a sudden it looks like a fantastic season.
"Really enjoying competing with the top guys. Same again tomorrow."
Earlier, Cao Yupeng held his nerve to beat Judd Trump 6-4 to reach his first ranking final.
The Chinese was beaten by Trump at the same stage of the European Masters earlier this year, previously his best performance in a televised event, and gained his revenge here in Glasgow.
Trump had fought back to 3-3 from 3-1 but Cao took control once more and signed off with his fourth half-century of the match to set up a clash with Robertson.
It's been a dream week for the 27-year-old, who made a maximum 147 break in round one.
For the first time during the tournament, Trump found himself behind after the first frame and breaks of 51 and 88 saw him trail 3-1 at the interval.
Trump made breaks of 50 and 76 to draw level but Cao restored his two-frame advantage to move within one of his first major final.
A 53 break from Trump cut the deficit to one and he had chances to force a decider, before a classy 72 break under enormous pressure saw Cao wrap up a 6-4 success.
Afternoon session (1300 GMT)
Semi-finals (Best of 11 frames)
- Cao Yupeng 6-4 Judd Trump
Evening session (1900 GMT)
Semi-finals (Best of 11 frames)
- Neil Robertson 6-3 John Higgins
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