But the breakthrough didn't come until 45 seconds into the second period when Sigurdsson's deflected shot found its way into the bottom corner past Palace keeper Wayne Hennessey.
Palace pulled one goal back through Luka Milivojevic from the penalty spot in the final stages. Palace remain 14th, only three points from the drop zone.
"Cenk is direct competition for me at the top of the pitch, so, hopefully, that will push us both on to do better and score goals".
Christian Benteke then reminded the Blues of his aerial threat after Mangala had been forced off with a knee injury when Alexander Sorloth capitalised on a rare mistake by Coleman and crossed for the Belgian but he missed with his header.
His predecessor in the role of England manager, Crystal Palace's Roy Hodgson was singled out by Allardyce in a tasteless manner.
75' - GOAL! Everton 3-0 Crystal Palace (Davies): It's been a convincing second-half performance from the Toffees and now they have a third goal to celebrate! A fortunate bounce fell to Cuco Martina who took time to size up a clipped cross for Niasse who steered a header inside the near post to double the lead.
"He's got a great position at the club at the moment and that's a very hard decision for him to give up - I'm sure about that because Everton U23s is a very privileged position and he's done very well in it".
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