Everton added to their tally when Tom Davies found the back of the net for his first goal of the campaign and, despite Luka Milivojevic pulling one back from the spot for the visitors, it proved to be a comfortable afternoon for the home side in the end.
A frenetic five-minute spell saw both sides comes close through long-range shots, with Milivojevic sending a deflected bullet shot wide and Sigurdsson doing likewise from a similar position.
The first save of the match arrived shortly before the half-hour mark, as Wayne Hennessey adjusted well to get down and turn aside Idrissa Gueye's drive following some good work to create a yard of space.
Jordan Pickford also had one first-half stop to make, just about managing to get behind an awkward Cabaye shot that dipped in front of him to see the sides go into the interval level.
Everton, unbeaten in six against Palace prior to today, did have an injury blow to contend with before the break, however, as Mangala was unable to shake off a knee problem and was replaced by Ashley Williams.
Less than a minute of the second half was required for the Toffees to finally get going, courtesy of Sigurdsson's moment of quality on the edge of the box.
Niasse did well to pick out his teammate, who took one touch with his left foot to set himself up and then buried the ball past Hennessey via a small deflection.
One goal soon became two after Cuco Martina latched on to a loose ball and spotted Niasse, giving the striker - preferred to Cenk Tosun once again today - the chance to guide his header into the bottom corner from seven yards.
Palace had chances to force their way back into the game, seeing strikers Christian Benteke and Alexander Sorloth come close - the latter forcing a big save out of Pickford on his first outing in a Palace shirt.
A third Everton goal arrived 15 minutes from time to kill off the contest, however, as Sigurdsson pounced on the rebound after Hennessey denied Niasse to give Davies a simple finish.
Morgan Schneiderlin was then brought on to shore up midfield, greeted onto the field by a number of jeers from home fans due to a perceived lack of effort this term.
The visitors gave their opponents a little something to think about late on after Milivojevic converted from the spot, making it six goals in 11 outings - four of those pens - after the ball hit Williams on the hand inside the box.
There was to be no grandstand finish to the match, however, with Everton able to easily see things through to consolidate their position in the top half of the division.
EVERTON (4-2-3-1): Pickford; Coleman (Kenny 46'), Mangala (Williams 45'), Keane, Martina; Gueye (Schneiderlin 80'), Davies; Walcott, Rooney, Sigurdsson; Niasse
CRYSTAL PALACE (4-4-2): Hennessey; Fosu-Mensah, Tomkins, Ward, Van Aanholt; Townsend, Cabaye, Milivojevic, McArthur; Sorloth, Benteke