In a straight shootout to see who would qualify as Group A runner-up behind Stuart Bingham, Robertson went 2-0 down and, knowing a draw would send Ding through, proceeded to mount a dramatic fightback.
Both players missed the deciding black in a tight opening frame before Ding finally put it away, with the Chinese player then moving two frames up with a break of 95.
Ding also took a big lead in the third frame but Robertson fought back to keep his hopes of progression alive with an audacious double on the black, and a run of 70 next time out levelled the contest.
A loose safety from Ding let Robertson edge ahead at 3-2, and the Australian then erased a 57-point deficit in the sixth frame to complete the turnaround.
"In the first few frames I had a pretty horrible run of the ball," he told Sky Sports. "Tonight [Thursday] looked like it wasn't going to be my night but I fought back really well and capitalised on some of Ding's mistakes.
"But if Ding doesn't get the kick on a red in the last frame then I go out. I've missed out on making the semi-finals of the Premier League by a frame twice already, so I didn't want to make it a third time."
Earlier in the evening John Higgins failed in his bid to finish atop Group B as he suffered a 4-2 defeat to Peter Ebdon, who was already out of semi-final contention but ended his campaign on a high note.
After Ebdon had won a scrappy first frame Higgins, who had already qualified for the knockout stages, brilliantly reeled off consecutive clearances of 125 and 134 to take the lead.
But the 2002 world champion managed to check his opponent's momentum, winning the next two frames to put his nose back in front before completing the victory with a break of 81.
Higgins will face Bingham in the semi-finals while Robertson will take on Judd Trump.