The former Middlesbrough striker justified his inclusion after making a telling contribution in the Carabao Cup in midweek, and he secured a vital three points with a 25th-minute spot-kick.
In a game lacking in real quality, the hosts did enough against their toothless opponents who seemed short of ideas, despite hitting the post late on through Marcus Browne.
The victory lifts Blackburn off the bottom of the league and above their winless opponents.
Pressure now intensifies on rookie manager Jonathan Woodgate, whose Boro side have yet to taste victory in four games in all competitions this season.
It is also the first time Middlesbrough have failed to win any of their first three league fixtures in 15 years.
Tony Mowbray made four changes from the league defeat at Fulham, with Greg Cunningham making his league debut; Anfernee Dijksteel made his first Championship start for Boro – one of two changes.
Boro started well in the early exchanges, with Lewis Wing poking a 20-yard effort wide, but the visitors were poor for the most part and Blackburn were in control.
Although Graham just failed to get a telling connection on Bradley Dack's cross in the 14th minute, he did not have to wait long for a glorious opportunity.
Dijksteel, making his first league start for Boro, needlessly tugged Graham back in the area with very little danger apparent.
And Blackburn's player of last season confidently sent Darren Randolph the wrong way in the 25th minute – the first league goal scored by a Blackburn player this season.
Jonny Howson did register a shot on target for Boro at the end of the half, but that could not mask a poor first-half performance.
Another former Boro favourite went agonisingly close to piling on the misery for the visitors at the start of the second half, but Stewart Downing's superb curling effort whistled past the post with Randolph well beaten.
Woodgate's men showed signs of life in the 74th minute though when an incisive cross from Paddy McNair left Christian Walton in no man's land but Browne could only strike the woodwork with his back-post volley.
Rovers almost put the game to bed minutes later when John Buckley's cross found Joe Rothwell at the back post, but Randolph pulled off a stunning save, sticking a palm out to repel the danger.
Substitute Buckley directed a half-volley over the crossbar in the closing stages, but it hardly mattered as Rovers held on relatively comfortably.