Gestede’s hat-trick of headers would have been enough but the visitors’ stand-out player, Michail Antonio, sealed a brace of his own by equalising in the final two minutes.
Neither side could make the play-offs before the game but contributed to an entertaining afternoon that began with Gestede capitalising on a defensive error in the third minute.
Antonio equalised with a header of his own soon after before Gestede powered home another header 10 minutes from the break.
Henri Lansbury restored parity on the stroke of half-time and, although Benin international Gestede struck again with eight minutes left, Antonio had the final word with his 15th goal this season.
Rovers have won just one of their last six Championship outings.
Gestede was brought into the starting line-up as one of four changes, while Forest made six alterations from their midweek defeat to Watford, which included recalling Jamaal Lascelles in place of the suspended Kelvin Wilson.
Lascelles’ first notable contribution was calamitous as he left a blocked clearance for goalkeeper Karl Darlow in the third minute and the miscommunication allowed Gestede in to head home.
The lead only lasted four minutes as Modou Barrow cut in from the right and floated in a pinpoint cross for Antonio, who headed home from 12 yards.
Chances flowed freely early on, with Lansbury forcing Eastwood into a fine point-blank save after a cross was only half-cleared, and at the other end Craig Conway unleashed a low drive from 20 yards that Darlow did well to smother in a pulsating opening 15 minutes.
Forest went agonisingly close in the 27th minute when Barrow curled just over, and again soon after but Eastwood got something on Lansbury’s shot.
And they were made to pay for their profligacy in the 35th minute when Conway’s deep cross found Gestede, who powered an unstoppable header past Darlow.
But the lead lasted just 10 minutes as Forest levelled on the stroke of half-time when Antonio again caused mayhem and fed the onrushing Lansbury, who coolly slotted home in the area.
Although less frenetic, the second half saw a Ben Marshall header cannon off the crossbar, while Barrow’s header drifted just wide.
Blackburn looked to have won it eight minutes from time when Gestede completed his second Rovers hat-trick by out-jumping two players at the back post to head home Conway’s cross for his 19th of the season.
But Forest hit back with two minutes to go as a poor clearance fell to the game’s other outstanding performer in Antonio, who hammered home an unstoppable 25-yard drive to defeat Eastwood.