A game of few clear-cut chances was settled in first-half injury time by Arter’s left-foot effort from just outside the penalty area which flew into the top corner of the net.
It gave Fulham a third straight victory and moved them to within four points of second-placed West Brom, who host Derby on Wednesday.
A first defeat since the restart for Forest is likely to end their hopes of catching the top two and mean they have to settle for a play-off spot.
The hosts made two changes as Tiago Silva and Sammy Ameobi were restored to the starting line up, with Ryan Yates and Joia Nuno Da Costa among the substitutes.
There were three changes for Fulham. One was enforced after Tom Cairney suffered a knock against Birmingham, while Anthony Knockaert and Cyrus Christie dropped down to the bench. Joe Bryan, Neeskens Kebano and Saturday’s match-winning goal scorer Joshua Onomah were recalled.
A bright start to the game saw both sides exert some early pressure with a couple of corners apiece.
The first real chance came after 17 minutes after a mistake by Tim Ream, who was captaining Fulham in the absence of Cairney, mid-way inside his own half.
Ream’s error allowed Lewis Grabban a run towards the penalty area with only Michael Hector between himself and goalkeeper Marek Rodak. But Hector stood his ground as Grabban attempted to barge past him and the Forest striker’s shot was easily fielded by Rodak.
Fulham threatened for the first time as the half-hour mark approached. A driving run from Bobby Decordova-Reid saw him slalom past a sliding Ben Watson challenge before unleashing a swerving effort from 25 yards that dipped just over the crossbar.
Grabban had another chance at the end of the first half following some good work down the right by Matty Cash, but once again he was unable to make the desired contact and this time the ball dribbled harmlessly wide.
Arter had no such problems finding a clean strike moments later. The midfielder attempted a pass just outside the box but the ball deflected back to him off Watson. Arter then decided to shoot, sending a left-foot shot arrowing into the top corner of the net.
Forest responded to the setback positively at the start of the second half, putting their opponents under pressure with a succession of corners, but it was not until the 65th minute that they worked Rodak.
Alfa Semedo sent in a shot from the edge of the area but the Fulham goalkeeper held on to it well. Shortly afterwards, Oliveira Ribeiro found himself in a promising position but was unable to keep his effort down.
Bryan did likewise at the other end before Knockaert sent a shot skidding along the rain-soaked surface and into Brice Samba’s gloves.
It was end-to-end as the game reached the final stages and Rodka had to be alert to catch Da Costa’s looping header.
Forest pushed for an equaliser but it was not forthcoming and Fulham defending manfully for what could prove to be a crucial victory.