The 11-10 favourite, who also won over the same mile and two furlongs at Lingfield in February, galloped to victory by a length and three-quarters.
Absolute Blast (7-1) came home strongly to take second ahead of French outsider Allez Henri (25-1) in third.
Sovereign Debt (8-1) won the Mile by a neck from Nimr (14-1).
The eight-year-old grey, runner-up for the last two years, swept through in the final furlong to catch clear leader Salateen - who finished third - handing Ruth Carr her biggest win as a trainer.
After a sedate early pace in the Easter Classic, Paul Hanagan sent Third Time Lucky ahead of the field but Ryan Moore took up a prime position on Convey, tracking him and the mare Elbereth.
Rounding the home turn it was clear Convey had plenty to give and Moore said: "Things haven't always been straightforward with him, but I think he really enjoys the surface and he's grown up.
"He had too much class for them today."
Sir Michael Stoute's Convey secured a comfortable win in the Easter Classic, the feature race on All-Weather Championships Finals Day at Lingfield.