Lacklustre Rovers, now without a win in nine games, struggled to contain Everton at Goodison Park and were punished by Osman's deflected shot after 54 minutes.
The visitors hardly tested home goalkeeper Tim Howard and Baines put the game beyond them with a 75th-minute penalty after Phil Jones fouled Seamus Coleman.
Everton, now unbeaten in seven, moved within a point of sixth-placed rivals Liverpool.
They went ahead when Magaye Gueye took the corner short to Osman, who sidestepped Ruben Rochina and fired in a shot which flew in after a deflection off Christopher Samba.
Rochina was booked for a rash challenge on Tony Hibbert and another bad tackle, this time by Phil Jones on Coleman in the box, put the game beyond Blackburn as Baines stepped up to fire the penalty into the roof of the net.