‘The Asset’ triumphed 5-2 in his all-or-nothing clash, which set up a second round meeting with James Wade.
Nicholson had already claimed an impressive win against Kevin Painter but lost to Phil Taylor going into the decisive Group A match.
And a clinical display of finishing saw the Australian progress.
“I knew I’d have to dig in to get the right result and that’s exactly how it went,” admitted Nicholson, who landed five out of seven double attempts.
“It was a big challenge to get out of this group but I’ve done that and now it’s on to another big challenge in trying to beat James Wade.”
Nicholson hit a 180 in the opening leg, which he won on double eight before doubling his lead on tops.
Kellet halved the deficit but the former Players Champion produced a leg of real quality to restore his two leg advantage, hitting another maximum as he went out in 11 darts.
Kellett cleaned up 78 to stay in touch but Nicholson closed out the match in ruthless fashion, taking out 52 and 81 to book his place in the last 16.
By Chris Murphy