Jimenez struck late in the first half after Douglas Luiz was adjudged to have fouled Brazilian winger Kevin.
Forest had travelled to west London on Monday night knowing a victory would have lifted them above Fulham into the relatively calm waters of 15th place.
But after a fourth defeat from four Premier League trips to Craven Cottage, the Reds remain just one place above the drop zone, albeit with a healthy five-point cushion between them and West Ham United.
Forest's best chance of the first half fell to striker Igor Jesus, who illustrated why he only has one league goal to his name this season by blazing high over the crossbar.
The watching Paul Clement, Carlo Ancelotti's assistant for the Brazil national team, is unlikely to have been impressed.
Fulham eventually began to threaten as halftime approached, with Antonee Robinson overlapping and pulling the ball back for Sasa Lukic, who dragged his shot wide.
They came even closer moments later when another Robinson cross was headed into the side-netting by Jimenez.
Then, in first-half added time, the grounded Luiz attempted to hook the ball away from Kevin, only to catch the winger on the heel.
The incident looked similar to one at Everton on Saturday, when Arsenal defender William Saliba caught Thierno Barry but no penalty was given.
However, "the contact was sufficient for a foul" was the VAR's verdict this time and Mexican frontman Jimenez duly stepped up and then stuttered before sending Forest goalkeeper John Victor the wrong way.
It was Jimenez's fourth goal of the season and his 11th successful Fulham penalty from 11 attempts.
After the break Cottagers keeper Bernd Leno got down well to fend away a stinging drive from Neco Williams and held another from Murillo.
But it was Fulham who came closest to finding the net again, with Jimenez glancing Kenny Tete's inviting cross wide when it looked easier to score.
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