The visitors to Laing Park took the lead after 18 minutes and threatened to spring a surprise.
But Phil McGuire’s side were having none of it and raced into a 4-1 lead thanks to goals from Ryan Roche, Connor Coupe, Pat Martin and Dale Reid.
The home side never looked under a great deal of threat despite Letham reducing the advantage late in the game.
This weekend Panmure are at home again when they host Dundee North End.
Kick-off at Laing Park is 2.30pm.
As well as Panmure, there were weekend wins for Dundee East Craigie, Arbroath Victoria, Forfar United, Lochee United, Forfar West End and Kirriemuir Thistle.
Selected fixtures for this weekend see Arbroath Vics host Scone Thistle, Forfar United travel to Blairgowrie, Forfar West End welcome Dundee Dowfield and Kirriemuir Thistle are at home to Dundee Violet.