Callum Smith scored a late winner for the Pars in a 2-1 victory over their Championship rivals at the Tulloch Caledonian Stadium.
Partick Thistle thrashed Stranraer 5-0 at Stair Park and Queen of the South saw off Stenhousemuir 3-0 at Ochilview.
Queen's Park caused an upset by beating Ayr United on penalties after a 0-0 draw at Hampden while Alloa Athletic defeated local rivals Stirling Albion 3-1.
Annan Athletic notched up a 4-0 win over Celtic Colts and Falkirk defeated Rangers Colts 2-1 at Forthbank. Ross County beat Hearts Colts 2-1 at Tynecastle and Raith Rovers beat Aberdeen’s U21 side 3-1 but there was better news for Hamilton’s youngsters, who dismissed Clyde 4-1.
The match between Livingston Colts and Forfar Athletic was abandoned due to a power failure.
There are four more ties on Wednesday night and the draw for the second round takes place on Thursday at 1.00pm, live on the SPFL Facebook page.
Full list of Tuesday's IRN-BRU Cup first-round results and scorers
