Robertson's historic 100th ton came in the 22nd frame as he potted 15 reds with colours, added the yellow, then potted the green to bring the break to 101. The Australian celebrated in ecstasy at what he described as one of the greatest moments of his career, as the Crucible crowd rose to their feet to congratulate his remarkable achievement.
Robertson had long since smashed the record for the most centuries in a season - 61 set by Trump last term. But to reach the landmark ton of tons has been his goal for the past few months, and he achieved in on the perfect stage in Sheffield. When he missed a simple black on 94 at the end of his second round match against Mark Allen, then looked in danger of defeat against Trump, it seemed he might be marooned on 99. But the world number one kept his composure to reach the milestone and deserves the acclaim he will receive. Only 52 players have made 100 centuries in their whole career, so to do so in a single season is astonishing.
"It was great that it came at one of the most crucial times of the match," said Robertson. "I wasn't even thinking about the century until there were only a few balls left and the frame was finished - then I really went for it. I played a good shot on the last red, and then I couldn't miss the green. I would rather make the century of centuries here than a 147. I've made a couple of 147s and it's nowhere near the same achievement.
"Nobody will ever achieve 200 centuries - that would be impossible. For me to be the first player to achieve 100 centuries in a single season is a great honour. It may raise the bar for break-building - the players might try a bit harder when they're on 70 or 80. Stephen Hendry was the one who always tried to clear up no matter what, and that was the approach that I've taken all season."
The century break came in the midst of a classic encounter, as Robertson came from behind to earn a semi-final meeting with Mark Selby. It will be a repeat of the UK Championship final which Robertson won 10-7. The Cambridge-based left-hander needs to win two more matches to capture his second world title, having lifted the trophy in 2010.
Trump led 9-6 going into the final session, but Robertson started strongly tonight with a break of 52 to take the first frame, then made a 40 clearance to nick the second. Trump responded by taking the next two with a top run of 55 to make it 11-8 at the interval.
In frame 20, Trump went in-off the last red, escaping from a snooker, and Robertson took advantage to close the gap. He then made a break of 70 to draw within a frame, before the dramatic 101 got him level for the first time since 1-1.
The adrenaline rush might have distracted him, but after a few minutes outside the arena, Robertson quickly regained focus. He took frame 23 with runs of 33 and 31 to go 12-11 ahead. Robertson led 43-0 in the next when he went in-off, giving Trump the chance to clear up. But the Bristolian missed the black off its spot with one red left on 31, and Robertson added the points he needed, executing fine pots on green and brown.
"In the first session I was getting very frustrated," said 32-year-old Robertson. "My focus was on the centuries and not the match. I lost my concentration and he played really well. I deserved to be behind in the match - I played way too slow. I was grinding out the first two sessions - like I was walking through mud. Tonight was a perfect performance and that's how I should have approached the start of the match.
"Best of 33 with Mark Selby is going to be really tough. I can't allow myself to get bogged down so I have to approach the match the same way I did tonight. When I'm playing really well, I'm very difficult to beat."
Trump said: "I felt in control. He played some good stuff towards the end, but I always felt like I was going to get another chance.
"There were a few distractions for both players towards the end which was a bit unfair. On one shot, the commentators were making the crowd laugh and he missed, which was disappointing because it was a good game other than that.
"There was a lot of noise in the crowd - you can expect that. Neil got put off a few times and so did I, so it's frustrating - especially that last black that I missed.
"You're never going to get an easy game here, especially in the quarter-finals. I knew he wasn't going to give in, he was going to stick to his game plan. I'm just disappointed that at 11-8 I didn't get any chances.
"Neil making 100 centuries doesn't mean anything to me. I congratulated him at the end of the match - that's all I could do. He likes to show his emotions and the crowd can enjoy that sometimes, so I've got nothing against him doing that.
"If he plays like that, he'll have a good chance. If he gets to the final, Ronnie won't enjoy playing against him."
Robertson's centuries this season, event by event:
Bulgarian Open: 7
Wuxi Classic: 4
Australian Goldfields Open: 5
Shanghai Masters: 2
Indian Open: 5
Ruhr Open: 6
Kay Suzanne Memorial Cup: 5
International Championship: 10
Champion of Champions: 6
UK Championship: 8
Championship League: 22
German Masters: 2
Gdynia Open: 2
Haikou World Open: 5
Welsh Open: 2
China Open: 1
World Championship: 7
Ball by ball scoring and results from tournaments