After a goalless first-half, Everton eventually broke the deadlock thanks to Sigurdsson whose low shot from the edge of Palace’s box took a slight deflection off a defender before beating Wayne Hennessey in goal.
Everton doubled their lead in the 51st minute through Oumar Niasse who headed in Cuco Martina’s cross.
In the 75th minute, Tom Davies made it 3-0 as he slammed the ball into the net off Sigurdsson’s cutback after Hennessey failed to properly hold Niasse’s initial shot.
Palace pulled a goal back after Luka Milivojevic converted a 83rd minute penalty following a handball inside the box by an Everton player.
The win took Everton to ninth on 34 points while Palace are 14th on 27 points, just two points above the relegation zone.
At the London Stadium, Watford failed to replicate their big win against Chelsea as they were humbled 2-0 by West Ham United.
West Ham new signing, Patrice Evra, was an unused substitute in the game.
West Ham took the lead in the 38th minute thanks to former Manchester United striker Javier ‘Chicharito Hernandez who headed in Michail Antonio’s cross.
In the 78th minute, Marko Arnautovic made it 2-0 to West Ham as he smashed into the bottom corner from close range after the ball luckily deflected on to his path.
The Hammers are now 12th on 30 points with Watford 11th also on 30 points.
And at the Liberty Stadium, Swansea continued their resurgence under new manager Carlos Carvalha as they pipped Burnley 1-0.
South Korean star Song-Yueng Ki was the hero as he scored in the 81st minute.
The win moved Swansea up the table to 15th on 27 points and are they now unbeaten in their last five league games.
And at the Bet 365, Stoke missed the chance to move out of the relegation zone following their 1-1 draw against Brighton and Hove Albion.
Jose Izquierdo gave Brighton the lead on 32 minute before Xherdan Shaqiri equalised on 68 minutes.
Stoke had the chance to win the game in the 90th minute but Charlie Adam’s saw his penalty saved by Mathew Ryan.
The draw leaves Stoke in the drop zone in the 18th position with 25 points.
Everton 3 vs 1 C/Palace
West Ham 2 vs 0 Watford
Swansea 1 vs 0 Burnley
Stoke 1 vs 1 Brighton