In-form winger Jack Harrison restored parity for the hosts inside the first 20 minutes after Orel Mangala had opened the scoring for Forest, before Luis Sinisterra netted a stunning strike on the stroke of half time that proved to be the winning goal for Javi Gracia's men.
Leeds have now won two of their last three Premier League matches and have climbed up to 13th in the table, two points clear of the relegation zone.
As for Steve Cooper's side, they have extended their winless league run to eight matches and have slipped to 17th place, hovering just above the bottom three on goal difference.
In front of a fired-up Elland Road crowd, Leeds made a bright start to the contest, but it was Forest who came closest to opening the scoring in the eighth minute when Emmanuel Dennis struck the woodwork from close range after Morgan Gibbs-White had swung an inviting cross into the danger zone.
Forest were not ruing that missed chance for too long, though, as they broke the deadlock just four minutes later, with Mangala finishing off a brilliant counter-attacking move.
After receiving a pass on the left flank from Danilo, Dennis drove at the Leeds backline and side-stepped Luke Ayling before cutting the ball back to Mangala, who placed his first goal in English football into the bottom-left corner.
The Forest supporters were in fine voice in the away end after taking the lead, but they were silenced just eight minutes later when Harrison drew Leeds level with a powerful strike from close range.
Harrison, who had been involved in each of Leeds' previous four league goals at Elland Road (one goals and three assists), reacted to Keylor Navas spilling a shot from Marc Roca by pouncing on the loose ball and firing a strike beyond the Forest goalkeeper to restore parity for the hosts.
The Whites began to dominate proceedings midway through the first half and looked a constant threat in the final third, while Gibbs-White looked the most likely to create something for Forest on the break.
An acrobatic effort from Leeds centre-back Robin Koch following a corner was hooked off target before Patrick Bamford poked an effort on the stretch narrowly wide.
However, Leeds' persistence in attack eventually paid off as they took the lead on the stroke of half time courtesy of a moment of brilliance from Sinisterra, who cut inside from the left and curled a stunning right-footed effort into the far corner.
Leeds picked up from where they left off after the break, playing with a high tempo and causing more problems to a Forest side, who initially struggled to break out of their own half before the introduction of substitute Taiwo Awoniyi gave them a focal point to aim for.
Although the game gradually developed into an end-to-end contest, Leeds looked the most likely to score again and created the better chances in the final third, particular through Harrison and Sinisterra.
After Junior Firpo made a decisive tackle on Awoniyi at one end, Harrison dragged a shot wide at the other from a tight angle on the hour mark, before Brenden Aaronson teed up Sinisterra for a glancing header than flew narrowly wide of the far post.
Bamford then missed a glorious chance to increase Leeds' lead following a defensive mix-up from Forest, but the striker could only smash a half-volley across the face of goal and wide of the target.
Forest threw bodies forward in the final 10 minutes in an attempt to snatch a point, but Leeds defender well and held on to claim three valuable points on home soil.
Gracia's side will now turn their attention to Sunday's home encounter against Crystal Palace, while Forest will make the trip to in-form Aston Villa for their next match on Saturday.