The West Londoners were in control of proceedings from the first whistle but took a while to hit the front, although strikes from Alex Iwobi and Mexican Jimenez had the Cottagers two goals ahead after a first half in which the visitors failed to test Bernd Leno in the hosts' goal.
Half-time alterations from Forest boss Cooper did nothing to change the course of the contest, with Iwobi and Jimenez both securing braces in the second period, before substitute Tom Cairney scored in the closing stages to inflict even more pain on his boyhood club.
After ending up on the losing side of a seven-goal thriller with Jurgen Klopp's Liverpool on Sunday afternoon, Marco Silva made four changes to his starting XI, allowing Timothy Castagne to return at right-back at the expense of Kenny Tete, while Tosin Adarabioyo made his first league start of the campaign alongside Calvin Bassey in the centre of defence.
Under-pressure Cooper made five alterations to his side following the poor display at the City Ground against Everton on the weekend, allowing Divock Origi to make his full debut in the Premier League for the Tricky Trees, with Morgan Gibbs-White dropping out of the team for the first time since October 1.
Liverpool's cult hero Origi was the main protagonist alongside Fulham defender Bassey in the early stages as both enjoyed physical battles for the ball, however it was the hosts who assumed control of the proceedings from the first minute, with Forest looking to hit their opponents on the break.
Silva's men struggled to create much in the first 25 minutes but nearly took the lead when Andreas Pereira saw his free kick effort cannon off the post and behind for a corner, and it was questionable whether the outstretched Odisseas Vlachodimos had the shot covered if it had been on target.
The game burst into life from a Fulham perspective after Pereira went close from that set-piece, and it was not long before the Cottagers were ahead in West London, when Willian's inswinging delivery from the left found the run of Iwobi, who evaded the attentions of Harry Toffolo and produced a side-footed finish into the Forest net.
Heads appeared to drop immediately in the Forest camp following Fulham's first punch of the evening, and under five minutes later Silva's charges had doubled their advantage against their East Midlands opponents, with forward Jimenez bagging his first goal in front of the Craven Cottage faithful.
A loose ball found its way to Iwobi on the right flank, and the Nigeria international was quick to find Pereira in a pocket of space in the middle, before the former Manchester United man picked out the run of the Mexican, who fired a strike into the top-right corner past the onrushing Vlachodimos.
Considering that Forest had never previously come from two goals down to win a match in the Premier League, Cooper and his side had a mountain to climb in the second period, and the Welsh coach opted to make two substitutions at the break, allowing Gibbs-White and Ryan Yates to enter the play at the expense of Ibrahim Sangare and Nicolas Dominguez.
Unfortunately for those of a Forest persuasion in the capital, the visitors' half-time changes did not have the desired effect, and Fulham were quick to sail into a three-goal lead just nine minutes after the interval, as Jimenez rolled back the years to his Molineux days to seal a brace.
Pereira was afforded acres of space in the middle of the park to pick out the towering presence of the Mexican, who peeled off Forest centre-back Felipe, shrugged off the attentions of Ola Aina and calmly rounded the goalkeeper, before producing an audacious backheel finish into an empty net.
Following the third goal, the mood around Craven Cottage turned into one of celebration for the home supporters, while the away fans from the East Midlands were singing the name of under-pressure boss Cooper, who could pay for tonight's result with his job.
On an evening when Fulham players were breaking individual records, Iwobi bagged his second of the game to seal his first-ever brace in club football, with a delicately-placed cutback from Welshman Harry Wilson allowing the former Arsenal and Everton attacker to finish past the Forest keeper.
The Cottagers' club captain Cairney was the next name onto the scoresheet in an enjoyable second half for the hosts, with the 32-year-old scoring his first league goal of the 2023-24 season against his boyhood side.
After making the net ripple on three occasions in three-straight league matches for the first time since the 1960s, Fulham are up to 12th in the Premier League standings, with the Whites back at the Cottage on Sunday afternoon when they will host David Moyes's West Ham United.
Whether Cooper takes Forest across the Midlands to clash with Wolverhampton Wanderers on Saturday is a matter for the hierarchy at the City Ground, however one certainty is that the Tricky Trees remain just six points above the bottom three following another limp away performance.No Data Analysis info