Heidar Helguson's ninth goal of the season had given Cardiff the lead before Darius Henderson was sent off for elbowing the veteran striker, Gestede then sealed the win with his second-half brace.
Henderson had missed Forest's best opportunity when he failed to convert from close range, while Lewis McGugan had an effort ruled out for a foul on Aron Gunnarsson as they dropped out of the play-off places and their 10-match unbeaten run ended.
Watford's defeat at Peterborough means Championship leaders Cardiff are now 12 points clear of the third-placed Hornets with four games remaining. A draw against Charlton on Tuesday will be enough to secure the Welsh club's return to the top flight after a 51-year absence.
The home side took the lead in the 26th minute. Kim Bo-Kyung won a free-kick after fooling Greg Halford, and the defender then lost Helguson from Craig Bellamy's free-kick for the striker to nod home at the far post.
McGugan thought he had levelled the scores just three minutes later when he got the better of Gunnarsson and curled home, but referee Andre Marriner ruled he had fouled the Iceland international.
Henderson then passed up a glorious chance. David Marshall saved Henri Lansbury's strike but the ball worked its way to the striker for what should have been a tap-in. But he stood on the ball and could not recover in time to prevent Marshall gathering.
Henderson was dismissed with just three minutes off the first half remaining, receiving a straight red for a blatant elbow on Helguson. Things got worse for Forest when Greg Halford was carried off two minutes after the resumption, having been caught in the face by Gestede's leg as he attempted a clearing header.
Cardiff were by now firmly in control and their second arrived on the hour. Bellamy curled a free-kick against the post and when the ball fell to Andrew Taylor, Gestede was on hand to convert his cross from close range.
Six minutes later and it was 3-0, Bellamy supplied the corner and Gestede once again made no mistake with his header to delight the record crowd at Cardiff City Stadium. Bellamy hit the outside of the post with the goal gaping as Cardiff cruised.