The striker came on as a second-half substitute to score Blackburn's fourth from Mauro Formica's assist.
Kilmarnock took the lead when, from Paul Heffernan's 10th minute cross, Grant Hanley diverted the ball into his own net.
However, Rovers were level two minutes later when Patrick Ada handled and David Dunn netted from the spot.
And it was soon 2-1 to the visitors when home keeper Kyle Letheren blocked Dunn's shot only for Jason Roberts to pounce on the rebound.
Rovers were awarded a second penalty on 31 which Roberts fired home after the striker had been held back as he raced into the area.
Killie's Paul Heffernan had an effort ruled out for offside while James Drayton was denied by visiting keeper Paul Robinson.
With 66 minutes on the clock, Goodwillie was brought on for his debut and on 75 he netted from close range after latching on to Formica's header.
Killie almost grabbed a late consolation when Manuel Pascali's shot was cleared off the line by Bruno Ribeiro.