The up-and-coming
Australian star was pulled back from 9-3 to 9-6 but secured victory in the 16th
frame to secure a last 32 spot at the Crucible in April.
Robertson also now looks sure to feature among the top 16 in the official
rankings next season.
The Melbourne left-hander, based in Cambridge during the season, compiled
breaks of 78, 74 and 117 as he surged 9-3 ahead. Kent-based Greene had earlier
made a 132 and found his range to pull back three frames with a top run of 76.
But Robertson made a 56 to take control of the next and sealed it on the
colours.
"I went for a risky red at 9-3 up, missed it and it looked like I might
pay for it," said the 24-year-old Aussie, who lost 10-7 to Stephen
Hendry on his Crucible debut last year.
"Gerard was completely relaxed at 9-3 down and started going for
everything so it was getting a bit edgy and I was relieved to finish it off.
"I was over the moon to draw Hendry last year because I’d always wanted to
play him, especially at Sheffield. But this time I would prefer to avoid him,
as well as Ronnie O’Sullivan and John Higgins. I want the chance to get used to
the atmosphere there."