South African McCarthy opened the scoring after 29 minutes with Derbyshire rounding the victory off ten minutes from time.
McCarthy - reportedly a target for Chelsea this summer - was on hand to convert a cross from Morten Gamst Pedersen just before the half hour.
Mark Hughes' men held their lead comfortably without quite getting out of second gear and young striker Derbyshire sealed the victory on 80 minutes when he drilled in a 25-yard shot via hapless keeper Vaidas Zutautas.
Partizan UEFA Cup ban confirmed
It was Rovers who had a great chance to take an early lead when Chris Samba rose unmarked to meet David Bentley's eighth-minute corner, but his header was wide of the goal.
Just two minutes later Jason Roberts tried his luck from long range but the striker's shot flashed over the crossbar.
It was not until 19 minutes later that Hughes' men had another real chance when Andre Ooijer was fouled on the right-hand side of the area.
Pedersen played a neat one-two with Ooijer from the free-kick and McCarthy was on hand to meet the cross from six yards.
The visitors, who reached the last 32 of the UEFA Cup last season, were lucky to escape in the 32nd minute when Bobi Bozinovski was sent clean through with just Brad Friedel to beat but his effort finished wide of the right post.
But Blackburn began the second half strongly and would have doubled their lead but for brave blocks denying McCarthy and then Aaron Mokoena in the 47th minute.
They eventually scored when Mokoena found Derbyshire, who drilled a powerful shot home from long range.
The second leg will be played at Ewood Park next Saturday.
Partizan allowed to play
Intertoto Wrap: Hamburg through