Joe Lolley put Forest in front in the first-half before Grabban doubled the lead from the penalty spot. Stewart Downing reduced the deficit for Rovers before a superb second for Grabban in the second half.
A Joe Worrall own goal proved to be just a consolation for Blackburn as Forest climbed up to fourth in the Championship table.
Sabri Lamouchi made three changes to the side which defeated Wigan on Sunday, with Samba Sow returning from injury to take his place in midfield and Tiago Silva and Joe Lolley recalled to the starting 11.
There was an even start to the game as Blackburn looked slick with their passing while Forest showed plenty of attacking threat. Joe Rothwell fired over the bar following some neat footwork before Samba Sow could, and should, have put Forest into the lead as he headed wide following Silva’s left-wing corner on 16.
But on 22 minutes The Reds took the lead as Lolley cut inside from the right-hand side and curled a cross into the box which evaded everyone, despite Sammy Ameobi’s best efforts to get on the end of it, before nestling into the bottom corner of the net.
Just two minutes later and Forest had a golden chance to double the advantage as Chema played a fine through ball with the outside of his boot for Lolley, who controlled and rounded Christian Walton in the Rovers goal before being hauled down for a clear-cut penalty.
Up stepped Lewis Grabban who made no mistake from 12 yards, calmly and confidently firing into the bottom corner despite Walton diving the right way.
The Reds were in the ascendency but the visitors were allowed a way back into the game on 39 minutes as Adam Armstrong broke the offside trap, laid the ball back for Stewart Downing who sent an accurate strike into the top corner of Brice Samba’s net to reduce the arrears.
There could have been further goals before the break as a swift counter-attack ended with Lolley forcing a good low save from Walton, then Corry Evans had a golden chance to level but he was denied by Samba from 10 yards out.
The second half started with pressure from Blackburn as they looked for an equalising goal, with centre back Darragh Lenihan heading over the bar from close range.
On 55 the two-goal lead was restored following a fine counter-attack involving Grabban and Ameobi. Grabban held the ball up, played Ameobi in down the left who skipped past his man before delivering a pin-point cross onto the head of Grabban, who produced a superb cushioned header back across goal and past a defeated Walton.
It was almost four for Forest just after the hour mark as this time Grabban was the provider, beating his man to get to the byline and square a pass back for Ameobi but it was just out of the winger’s reach and Rovers were able clear.
Once again, however, Forest were pegged back as Elliott Bennett’s cross from the right was turned into his own net at the near post by a sliding Joe Worrall on 71 to give Rovers a boost heading into the closing stages of the game.
But Forest held firm, repelling any threats that came their way as they game headed to a close, with Tiago Silva forcing a fine save from Walton from a free kick the last of the goalmouth action.
Another big three points for Forest, a third victory in a row and the perfect start to 2020.
Forest: Samba; Cash, Worrall, Figueiredo, Chema (Robinson 27’); Watson (c), Sow (Semedo 67’); Lolley (Adomah 87’), Silva, Ameobi; Grabban
Subs: Smith, Carvalho, Jenkinson, Dawson
Goals: Lolley 22’, Grabban pen 25’, 55’
Booking: Sow 45’
Blackburn: Walton; Bennett (c) (Graham 72’), Lenihan, Adarabioyo, Bell; Travis (Chapman 65’), Evans, Downing, Rothwell; Armstrong, Brereton (Gallagher 65’)
Subs: Leutwiler, Williams, Johnson, Buckley
Goals: Downing 39’, Worrall own goal 71’
Booking: Bell 90’
Referee: Darren Bond
Attendance: 27,073 (883 away)