The Leeds veteran cueman got the better of Australian potter Robertson, winning 6-3 at the York Barbican.
Having dropped off the tour last year, Lines now competes as an amateur but the 46-year-old established a 3-1 lead before Robertson clinched frame five.
Lines, though, was not be denied, clinching the next to restore his two-frame cushion.
And even when Robertson replied with a swift 72 to make it 4-3, Lines showed his experience of decades on the circuit, by keeping his nerve.
He clinched victory with a 57 break to move into the second round, alongside his son Oliver, who is a rising star in the sport.
Lines said: “I’ve beaten a lot of the top players - (John) Higgins, Ronnie (O’Sullivan) - but this is probably the most pleasing result I’ve ever had.
“It was a daunting task to play the defending champion.
“A lot of people say you’ve got nothing to lose. I wanted to go out and relax and at least give a good account of myself. In my heart of hearts I wasn’t really expecting to win, but I did play quite well tonight.
“I’m pleased with how I held myself together because Neil’s obviously a fantastic player. Hopefully I can win a few more matches.”
He plays Chris Wakelin next, at the weekend, while Australian Robertson heads back to his Cambridge home.
Robertson led the praise for Lines, saying: “I got old-schooled today. His safety was absolutely incredible, probably some of the best safety I’ve come across for quite some time in terms of him denying you an opening. He didn’t make a whole lot of big breaks but he didn’t have to.”
Lines is nominally considered an amateur, although that does not stop him earning prize money, and he pockets a modest £5,000 for now after one of the best wins of his career.
It’s another success for the Northern Snooker Centre where the Lines father-and-son pair train.
But there was to be no fairytale repeat for another Northern Snooker Centre potter, as David Grace bowed at the the first round stage.
His 6-2 first-round defeat to rising Chinese star Zhao Xintong came on a frustrating day for Yorkshire’s snooker stars - until Lines’s late, late show - as Sanderson Lam and Christopher Keogan were also knocked out at the York Barbican.
Grace started well against Zhao – taking two of the opening three frames to establish an early 2-1 lead – only for the precocious 19-year-old to respond in style.
He reeled off five frames on the spin as breaks of 61, 53, 66 and 64 helped do the damage to leave his opponent heading back to Leeds early.
Grace’s exit was a far cry from 12 months ago when, seeded 80th, he beat Andrew Higginson, Robert Milkins, Jack Lisowski, Peter Ebdon and Martin Gould in an incredible run to the semi-finals – where he went down 6-4 to Liang Wenbo.
And the 31-year-old couldn’t help but reflect on his failure to match those achievements this time around.
“Doing so well here last year does make it a little bit disappointing to go out early this time,” said Grace.
“I wasn’t waiting all year for this to come round though, I’ve been trying my hardest in every tournament.
“But it would have been nice to get through to the TV stage, to at least feel like I was part of the tournament but it wasn’t to be.
“I really enjoyed playing in the TV set-up last year and getting to the latter stages, so I want to do it again at other events.
“I don’t feel like I’m that far away. It’s just a few missed shots here and there at key moments in the game.”
Zhao is widely considered one of the hottest prospects in snooker and reached the last 16 of the 2013 International Championship as a 16-year-old after being given a wildcard entry.
The Chinese player is a better cueman than his ranking of 88 in the world might suggest and after seeing him first-hand, Grace concedes he would have preferred a different opponent in the opener.
“It wasn’t great from me but I didn’t do that much wrong – he was just potting them off lampshades! I just genuinely couldn’t keep him safe,” added Grace.
“By the end I was going for mental shots myself because I thought ‘if this is my last shot, I might as well just go for one’.
“You possibly curse your luck a bit when you draw someone like him in round one. As the seedings were coming close, I could work out who it might be in my section of the draw, obviously he was the one to probably avoid. But I had half-chances, so I can’t complain.”
Grace’s fellow Leeds potter Lam suffered a different kind of defeat as he lost a nail-biting encounter 6-5 to veteran Dominic Dale.
Breaks of 72, 77, 54 and 113 ultimately weren’t enough for the 22-year-old, who squandered a 5-4 lead against a man ranked 51 places above him.
Meanwhile Doncaster’s Keogan ran into an unstoppable force in the form of Ali Carter, as the Essex cueman racked up two centuries and four further half-centuries in a 6-1 victory.
And the 24-year-old claims losses like that are a learning curve in his first year on tour.
“Ali has played really well there, but I had a couple of half-chances in the first couple of frames and against the top players you have go to at least make something of them,” Keogan insisted.
“If you don’t do it, you don’t experience it, you can’t learn from it. Hopefully I am slowly but surely moving in the right direction.
“Being from Yorkshire, this is one of the main tournaments you look forward to – I just wish I could’ve put a better display on.”
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