And after setting up a meeting against Yorkshireman Paul Hunter, the 21-year-old Scot thanked Griffiths for his part in the victory.
"I went to see Terry after the Welsh Open last month because I was getting to the point of chucking in the game," said Dott. "My results had been dreadful and I didn't even enjoy practice anymore. But Terry set me right on a number of things.
"Snooker is a mental thing and he put my head straight on a few matters. Much of the stuff I already knew but it was just good to talk with someone who has so much knowledge."
Dott, a professional since 1994, came from 4-2 down to beat 1991 world champion Parrott. A break of 107 in frame seven began the revival and he added a half-century in the eighth to level at 4-4. In the decider runs of 27 and 23 ensured Dott booked only the second quarter-final of his career.
Hunter, a second-round winner over Ronnie O'Sullivan, survived a comeback attempt by Dott's fellow Scot, Jamie Burnett, to win 5-4.
Burnett forced a decider after being 4-1 down but was denied at the last gasp by Hunter's run of 53.
Mark Williams stayed on course for a third successive ranking title thanks to his 5-4 win over Matthew Stevens.
"I don't know how I'm still here," said Welsh left-hander Williams, badly hampered by a chest infection. "But I guess winning becomes a habit."
Stevens had a chance to win the decider but on 29 he snookered himself on the pink. Williams eventually produced a 41 clearance started after he trapped his compatriot in a tight snooker.
Grand Prix champion Stephen Lee whitewashed Peter Ebdon who was clearly exhausted after his marathon match the previous night against Jimmy White.Reuse content