Trump's defeat means that the world's top three are already out of the tournament as Mark Selby and Ding Junhui have also been beaten.
The Englishman began well, with breaks of 93 and 78 seeing him open up a 2-0 lead over the Scot but Dott then upped his level and barely missed a ball as he flew over the winning line at York's Barbican.
He racked up five breaks of more than 50 and will next face Stephen Maguire in round four.
Dott won the 2008 World Championship title but has flown under the radar in recent times, and he admits it is nice to prove that he can still mix it with the best on the green baize.
"People ask if I still play snooker. Delivery men will still ask "are you still playing?", so it's nice to remind people that I am still around," he said.