Rovers had not tasted defeat in the previous nine meetings between these two sides – and had won three of their last four games on the banks of the River Trent.
They pushed hard to avoid defeat again, amid a nervy finale, but Sabri Lamouchi's side held out for a win that put them level on points with third-placed Brentford.
Joe Lolley had given Forest the lead before Grabban bagged his first from the penalty spot.
Samba Sow should have put Forest in front when he was allowed a free header from a corner, but guided the ball wide with the goal at his mercy.
But the game sprang into life as the home side netted twice in the space of three minutes.
The first came as Lolley capped off a flurry of sharp passing by cutting inside on the right flank and bending a left-footed cross-shot across goal.
Things got worse for the Blackburn keeper in the 25th minute, when he conceded a penalty.
Lolley rampaged into the box to get onto the end of a fine ball from Chema, beating Walton to the ball, before being felled by Rovers' number one.
Grabban made no mistake from the penalty, driving the ball low into the corner, with Walton diving the right way, but finding the shot just beyond his reach.
A poor first touch from Tiago Silva saw Forest spurn a decent opening – and it proved to be costly as Blackburn immediately countered and pulled a goal back.
Downing drove an emphatic finish high into the back of the net after he had been picked out inside the box by Adam Armstrong.
Lolley would have had his second of the game if not for a strong, alert save from Walton, diving low to his right.
But Brice Samba also had to block brilliantly with his legs when Corry Evans found himself with only the Forest keeper to beat at the other end.
Any nervousness from the home fans was addressed 10 minutes into the second half, when Forest broke decisively.
Ameobi carried the ball powerfully down the left before picking out Grabban's run to the far post with a precise cross – and the striker applied a delightful headed finish, back across goal and inside the post to make it 3-1.
Blackburn pulled a goal back when Elliott Bennett's driven low cross from the right was deflected into the back of his own net by defender Joe Worrall in the 71st minute.
Armstrong flicked a header over the bar as Blackburn pushed, but Walton also had to make an outstanding save to keep out a Silva free-kick.