The scoreline was not an accurate reflection of the balance of play, however, and Ton would have felt aggrieved not to have been leading before they fell behind against the run of play on 27 minutes.
Derek Gaston saved a Charlie Telfer effort but failed to hold, allowing Jamie Burrows to follow in and tap into an empty net.
Reserve coach David Hopkin made a change at the break, bringing on trialist David McNeil in order to switch to 4-4-2 formation.
The former Kilmarnock kid made an instant impression, and hit the post, had a goal ruled out for offside, and fired wide all within seven minutes of the restart.
But it was the hosts who scored again when Northern Irish youth international Matthew Clarke converted from the spot after Nicky Jamieson was penalised for a foul on Lewis Morgan.
Billy Kirkwood's side added a third four minutes from the end through Ben Reilly, who drilled past Gaston from 10 yards.
The margin of victory flattered the Ibrox men - something Kirkwood conceded: "To be fair, I thought they put us under pressure right from kick-off with the way they played the game."
Ton can no longer qualify for the semi-finals but play their final fixture on Monday 29 April when they travel to Lesser Hampden to face Queen's Park.
Kick-off is 7.30pm.