Last season’s Premier Division runners-up overpowered their Stirling and District League visitors and have been rewarded with a home draw against Grangemouth in the next round.
Yuill, who returned to the club over the summer form Salvesen, didn’t take long to net the opener for Alan McKay’s side as he profited from a neat inter change between Lee Edwardson and Chris Carins by netting a half-volley after just six minutes.
Three minutes later he was celebrating his second of the game, this time volleying in first time from Cairns’ throw-in.
Cairns made it three from the penalty spot after 11 minutes, before Michael Hornig slotted in from Sam Thompson’s pass to make it 4-0 inside 20 minutes.
Yuill volleyed in once more to complete his treble, with Cairns then making no mistake when Thistle were awarded their second penalty of the day.
Kincardine couldn’t cope with the Yuill and the physical striker netted his fourth with an effort from outside the box with 20 minutes remaining to cap an impressive showing in front of Scotland Amateurs boss Colin Macleod.
Elsewhere, Bank of Scotland Strollers put six goals past Sporting Saughton without reply away from home as they too made it through to the second round.
Jack Leslie put Anton Caballero through one on one with the visiting goalkeeper for the opener. His initial shot wasn’t dealt with properly and left Caballero with a simple tap in on his first game back from injury.
The winger then turned provider for Steven Lindsay ahead of the interval as he volleyed in number two.
Nick Perry then benefited from another Caballero assist to make it three, before Connor Preston’s corner-kick deflected off a Saughton defender and into the net.
Preston made sure the next goal was his, as Caballero made it a treble of assists, playing in Preston who found the net with just the keeper to beat. Lawry Ross wrapped up a dominant win when he lifted the ball over Saughton’s keeper and into the net after taking control of Ross McPherson’s through ball.