Captain Luka Milivojevic netted his seventh top-flight goal of the season from the penalty spot midway through the first half before Jeffrey Schlupp pounced on a rebound from a Batshuayi effort to double the lead in the second half and secure a vital three points.
Even though Palace had to wait for a second, it was in control throughout as Fulham fell to its eighth straight loss in a Premier League London derby and failed build on a 4-2 win over Brighton and Hove Albion in midweek.
Roy Hodgson had the luxury of leaving deadline-day signing Batshuayi on the bench until the 82nd minute, but the striker still had enough time to play a part in Schlupp's late clincher, as Palace won for the first time in four league games.
Aleksandar Mitrovic failed to take a golden early chance, sending a free header wide from six yards after being found by Joe Bryan's delivery.
That proved costly when Palace took a 25th-minute lead from the penalty spot. Cyrus Christie's handball while climbing to challenge Christian Benteke, who made his first start since September, gave Michael Oliver an easy decision, and Milivojevic found the net despite Sergio Rico getting a hand on his effort.
With half-time approaching, Benteke almost marked his return to the team with a goal when he sent an overhead kick off the crossbar having been picked out by Andros Townsend.
Rico made key second-half saves from Jordan Ayew and Schlupp, while Mamadou Sakho sent a header off target as Palace sought a deserved second goal.
That arrived with three minutes remaining when Batshuayi drew a fine save from Rico, allowing Schlupp to convert the close-range rebound as Palace cruised to victory, with Fulham failing to register a single shot on target in the contest.