Ryan McGowan and Tete Yengi scored the goals as Championship Livingston eased past third-tier Cove Rangers to secure a Scottish Cup quarter-final spot.
McGowan was in the right place in the six-yard box to turn in Reece McAlear's free-kick - his first of the season.
Another Adelaide-born player added the other two, as subsitute Yengi twice found the same bottom right corner to take his tally for the season to six.
Paul Hartley's Cove were trying to make history by reaching the last eight of the competition for the first time.
The visitors will look back on good saves by Jerome Prior from Findlay Marshall for spoiling that dream, and a header by Will Gillingham which drifted narrowly wide.
Cove's 11-goal striker Mitch Megginson also hit the outside of a post with a quickly taken effort from 20 yards.
There was no shortage of Scottish Cup-winning experience across the two sides.
Livi striker Stevie May lifted the trophy twice with St Johnstone and the centre-back pairing of McGowan and Danny Wilson were successful with Hearts and Rangers respectively.
As for Cove, manager Hartley was a Scottish Cup winner with Hearts and Celtic as a player, while captain Fraser Fyvie tasted glory with Hibernian, three years after lifting the FA Cup with Wigan Athletic.
Fyvie had one of the League 1 side's other good chances, shooting straight at Prior following a neatly worked corner kick routine.
The Frenchman's opposite number Nick Suman did a great job of keeping Cove in the tie when he dived high to his right to repel Dan Finlayson's bullet header.
But Suman could do nothing about Yengi's deadly strikes, one teed up by Danny Wilson's header and the other set up by Lewis Smith.