Alli put Dons into a commanding 2-0 lead at half-time before hosts County replied through Alan Sheehan with 20 minutes left.
But Alli wrapped up his treble in the dying moments to secure the win and MK Dons manager Robinson believes this is just the start for his young star.
"You forget how young Dele is and his maturity for a 17-year-old is there for all to see," Robinson said.
"He will be up there with Steven Gerrard, Wayne Rooney, Michael Owen - he is that good.
"I've been saying it for a long, long time. The kid is unique. I worked with young kids for seven years at Liverpool and I also worked with some of the best players in the world.
"What can't this kid do? He's good in the air, he's quick, he's 6ft-plus, he scores goals, he tackles - what more do you want?
"I am thrilled for him. His hat-trick capped off a great night for us. We've stemmed criticism but if you want to be successful we have to put this to bed very quickly.
"They will be happy but when we get back in to training it's straight back to work. We've two very important games on the horizon in Peterborough and Stevenage and it's important we keep the momentum going."
Alli made the most of some erratic Magpies defending to give the visitors the lead in the third minute, and he was gifted a second as Izale McLeod raced onto Hayden Mullins' backpass before squaring to Alli.
Notts County kept plugging away and were rewarded when Sheehan converted from the spot after Jordan Spence had handled, but Alli ended their comeback when he fired home in the last minute.