Substitute Joao Carvalho's stunning 72nd-minute strike gave the hosts a crucial lead in a game that had been drifting aimlessly towards a goalless draw.
Fellow substitute Karim Ansarifard then put the match beyond Hull's reach with a crisp follow-up just four minutes later.
And a home win was confirmed after 82 minutes when Joe Lolley scored from the penalty spot.
Blustery gales from off the River Trent made for difficult playing conditions, but Forest coped better for most of the game.
Yohan Benalouane and Tendayi Darikwa popped speculative efforts off target within the first five minutes, but Martin O'Neill's men were often compromised by a lack of finesse inside the final third.
Hull were hardly foot-perfect, either, but they at least grew in confidence as the match progressed.
And they had a rare glimpse on goal after 18 minutes when neat play on the left between Kamil Grosicki and Eric Lichaj gave Jarrod Bowen a sniff.
But Hull's leading goalscorer was always at full stretch just outside the six-yard box and scuffed the ball wide of Costel Pantilimon's right post.
Forest responded purposefully, with Leo Bonatini their most potent attacking outlet in the first half.
The Brazilian was twice given too much space in threatening positions and would have punished Hull had it not been for watchful defending from centre-backs Reece Burke and Jordy de Wijs.
Burke did especially well after 27 minutes when Bonatini's strong, goalbound hit from a central area was expertly blocked and diverted to safety.
Hull later gave Forest a minor fright when Grosicki tried his luck from the left corner of the 18-yard box, but Pantilimon was equal to it with a smart stop.
Counterpart David Marshall needed to be even brighter soon after the restart when Alexander Milosevic's downward header from Lolley's corner screwed towards goal - albeit with the help of a slight deflection.
But Marshall reacted sharply, and intelligently tipped the ball to his left and out of harm's way.
Hull manager Nigel Adkins had seen enough, and made a brave double substitution soon afterwards, with Marc Pugh and Chris Martin replaced by Fraizer Campbell and Evandro.
However, the introduction of Campbell and Evandro had the reverse effect as Carvalho dramatically gave Forest the lead.
The Portuguese, who replaced Daryl Murphy after 68 minutes, let fly with an exceptional right-footed effort which kissed both posts before hitting the net.
Hull hardly had time to regroup as Ansarifard, who came on for Bonatini, made it 2-0 after 76 minutes.
Lolley did all the hard work with a well-flighted strike which hit the bottom-right post. Ansarifard was well positioned to gather the rebound and made no mistake.
Forest were irrepressible by now and bounded into an unassailable lead when Markus Henriksen fouled Jack Colback in the penalty box.
Lolley did the rest with a sweet spot-kick to help secure his side what could prove to be three crucial points.
Hull have now lost four away games on the spin but manager Nigel Adkins refused to rule out an increasingly improbable tilt at the play-offs.
He said: “Before the game we were four points off the play-offs and now we are five points.
“We’ll reflect on this and prepare for the next game at top-of-the-table Norwich.
“We kept the home crowd quiet for long periods, but maybe we didn’t have that final decisive pass in the final third.
“The first goal was going to be decisive, but it’s fair to say it was a wonder strike from the lad.
“Sometimes it’s fine margins, but that’s given the home side the impetus to win the game - and then the second goal has taken it away from us.
“The scoreline’s the wrong one, but for long periods we were well and truly in the game.
“We wanted to win and we played some good football again, but you’ve got to go and score.”