After dominating possession, Everton took the lead in the 59th minute after Theo Walcott's shot was saved by Cardiff keeper Neil Etheridge. Sigurdsson was on hand to rifle the rebound into the net and put the Merseysiders in front.
Victor Camarasa went close for Cardiff with a rasping shot from distance 13 minutes later but Jordan Pickford dived smartly to his right to save it.
The visitors had a strong case for a penalty turned down in the 79th minute after Everton defender Seamus Coleman appeared to fell Gregory Cunningham in the box, but referee Paul Tierney waved away their appeals.
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"The most important thing was the three points. The first half was not the best performance, we started slow. We should do things faster against teams like this who are strong in defence," Everton boss Marco Silva said.
"It was different in the second half, we started to create more problems. But every moment we didn't score the game is always open, that is the Premier League."
Cardiff boss Neil Warnock, who will seek to bring in some firepower in the January transfer window, praised his players for their effort.
"If we were just a little bit more clinical... that's where we let ourselves down. That's why we are looking for players in January, but I can’t fault the players out there today," he said.
Cardiff's third defeat in four games leaves them third from bottom on eight points after 13 games, while Everton's fourth win in six puts them sixth on 22 points.
(Reporting by Philip O'Connor; editing by Clare Fallon and Tony Lawrence)
