Idrissa Gueye scored just before the half-hour mark to hand Everton the lead, before Dwight McNeil netted 14 minutes from time to secure a vital three points for the Toffees.
However, the victory was marred by a late injury to Beto, who received urgent medical attention after a clash of heads with Morgan Gibbs-White just prior to the full-time whistle, but the forward gave a thumbs up to the crowd after a lengthy stoppage as he was stretchered away.
Everton now sit five points clear of the relegation zone, having also played a game fewer than Luton Town, while Nottingham Forest remain just one point above 18th place and a further two ahead of resurgent Burnley who in 19th position.
Everton respond to heavy Chelsea defeat
In a game that had been billed as the 'Deduction Derby' courtesy of their points penalties from earlier in the season, both teams knew the importance of getting maximum points on the board.
Of all the players in their side, Everton supporters would have least expected a goal from Gueye, but it was the veteran midfielder who would put the home team in front after an uneventful start.
After the ball was only half cleared to him 30 yards out, Gueye took a touch before a low, bobbling effort from the edge of the area found its way into the far bottom corner.
Dominic Calvert-Lewin would soon come close to scoring a second with a deflected effort, Forest goalkeeper Matz Sels relieved to see it go just past the post, while the visitors were only denied an equaliser by a stunning save from Jordan Pickford who kept out Chris Wood's close-range volley.
Before the half-time whistle, though, Forest thought that they should have had a penalty, the ball hitting the outstretched arm of Ashley Young, but the referee and VAR ruled that the wide player and Callum Hudson-Odoi were too close together to deem it to be an infringement.
Everton see out key win
Like in the first half, the beginning of the second was somewhat scrappy, that suiting Everton given their position in the contest.
Chances for Forest had been few and far between but Gibbs-White should have perhaps levelled the game for his side on the hour mark, rather than skewing his strike off target.
As the game entered the closing quarter, Everton were doing an effective job in nullifying Forest's attacks, and they ultimately put the game to bed with 14 minutes left.
McNeil played a neat one-two on the edge of the area before producing a low shot not too dissimilar to that of Gueye's that found the bottom corner of the net via the inside of the post.
The match had been petering out as the game entered added-on time before Beto came off much the worst in a nasty clash of heads with Gibbs-White, the striker requiring nearly 10 minutes of treatment before acknowledging the crowd as he departed the pitch.
For a short moment, his wellbeing made Everton's success insignificant, but Sean Dyche and his squad were able to breathe a sigh of relief for footballing matters as they surged clear of the bottom three, at least in the short term.