Ding got off to a great start with breaks of 58 and 62 to take the opening frame but Robertson hit back with an unanswered 70 to level the match.
After sharing frames three and four, Ding seized the momentum by taking a topsy-turvy fifth 80-45 and followed it up with a break of 75 to leave him one away from victory before a century break assured his passage to the final four.
Barry Hawkins came from 4-2 behind to knock out world number two Mark Selby.
Selby had looked in total control after a series of impressive breaks, including a second frame century, but Hawkins hit back in stunning fashion as he levelled the tie with a break of 140.
And it was Hawkins who stole the decisive ninth frame, winning it 79-25 to set up a semi-final with Ding.
In the earlier matches Xiao Guodong and Michael Holt both reached the semi-finals of a ranking event for the first time.
Xiao delighted the home fans with a come from behind 5-4 victory against Mark Davies after having been 4-2 down at one stage.
The final frame provided drama as Davies was presented with a chance to come back from 61-0 down with 67 left on the table.
However, he accidentally ended up potting two reds at the same time which left him needing snookers which he never recovered from.
Things were easier for Holt, who enjoyed a straightforward 5-1 win over Kyren Wilson as he made his first semi-final 17 years after turning pro.
Holt produced breaks of 85 and 64 before a run of 80 in the final frame sealed the victory.
Xiao and Holt will now meet each other in the final four.
Xiao Guodong 5-4 Mark Davis
Michael Holt 5-1 Kyren Wilson
Mark Selby 4-5 Barry Hawkins
Ding Junhui 5-2 Neil Robertson