Making just his second appearance for the Championship side after joining on a season-long loan earlier this month, the forward clinically converted from close range to add Rovers' third of the game.
In doing so, Elliott became Blackburn's fourth-youngest goalscorer in their history at 17 years and 203 days.
He then provided an assist for Sam Gallagher late on to complete the afternoon's scoring.
ud83dudcab The fourth youngest scorer in #Rovers' history! #COVvROV ud83dudd35u26aaufe0f https://t.co/DhkaoqxiI4
— Rovers (Blackburn Rovers) 24th Oct 15:37
Speaking post-match, Elliott said: "The main result is the key thing here.