Mason defeated Jordan Boulton of Hollinwell 2up while Maxey defeated George Heath (Wakefield) 3&2 in the round of 64 on Thursday.
Thursday was a rather windswept third day of the English Amateur and first to be played solely at Moortown, after the former Ryder Cup venue jointly hosted the qualifying stroke play rounds with Headingley.
Hallowes’ Sam Bairstow, who played in the Open earlier this month, is also through to the last 32 after he defeated Max Hopkins (Bishops Stortford) 3&2. Bairstow now plays Harvey Byers of Walton Heath.
Bairstow admitted he was scrappy at the start, but conquered the howling wind and then closed the game out with birdies on his final two holes.
“I quite enjoy playing in the wind,” he said. “It gives you a lot more definition on the shots.”
But they are the only three Yorkshiremen to advance from the round of 64. Pannal’s Oliver White, Hickleton’s Luke Palmowski, Doncaster’s Joshua Berry (beaten 2&1 by Walker Cup player Jack Dyer) and Rotherham’s Jack Whaley were all eliminated.
In the women’s English Amateur it was the round of 32 on Thursday with Huddersfield’s Charlotte Heath a surprise casualty. Having set the lowest score at Moortown in the stroke play rounds, Heath was beaten 2&1 by Danielle Hardwick (Perrenporth).
There was an all-Yorkshire tie between Lily Hirst (Woodsome Hall) and Hannah Holden (Huddersfield), with the former coming out on top 3&2. Hirst now plays Annabelle Fuller (Roehampton).
Mia Eales-Smith will also play a last-16 tie today against Harriet Lynch (Thorndon Park) after defeating Caley McGinty (Knowle) by one hole.
Bethany Norton (The Oaks) was beaten on the final hole of her last-32 tie with Katy Yates (Clacton-on-Sea).