Marco Silva's men made it four straight league wins at Goodison Park thanks to Sigurdsson's seventh goal of the season after 59 minutes.
Michael Keane had a header saved by Neil Etheridge, while Andre Gomes - fit to play despite injury ruling him out for Portugal - fired against the side netting in an opening period that saw Cardiff's defence largely frustrate the hosts.
An excellent Sol Bamba goal-line clearance was all that denied Sigurdsson after Bernard had set up his left-footed effort from a tight angle.
But the Iceland international was not to be denied in Everton's next attack just before the hour mark. Following Richarlison's flick, Theo Walcott surged through on goal, and when his effort brought a one-handed save by Etheridge, Sigurdsson tapped in the rebound from 10 yards.
Having suffered a nasty blow to the head in an awkward landing earlier in the second half, Jordan Pickford did well to parry Victor Camarasa's strike as Cardiff sought a way back into the game in a brief spell of pressure which also saw an angry Greg Cunningham have a penalty claim denied after being challenged by Seamus Coleman.
That good fortune was all Everton needed to see out the victory, Ademola Lookman, Richarlison and Cenk Tosun forcing late saves from Etheridge in the closing stages, although Callum Paterson gave them one final scare with a header over at the death.
What does it mean? Everton building momentum
The solid if not spectacular win moves Everton above Manchester United in the table and builds on a solid run of recent results that has seen them lose just once in seven league games and steady the ship after a mixed start. Their home form will be a significant boost to Silva – stretching back to last season they have lost just one of their last 10 at Goodison Park in the top flight.
Cardiff's defence looked more resolute than it has done recently, but their problems are at the other end – 11 goals scored in 13 games the main contributor for their slow start to the Premier League campaign.
Sigurdsson shines again
As well as hitting the winner, Sigurdsson had Everton's best other opening with an effort cleared off the line, and also set up two chances for his team-mates. He continues to impress this year after being criticised in his first campaign following his big-money move from Swansea City.
Arter struggles to make an impact
Harry Arter returned from suspension for this encounter, but struggled to make an impact before being replaced by Junior Hoilett after 74 minutes. He created zero chances for his team-mates, and only had 10 total passes in the Everton half.
Key Opta Facts
- Cardiff have scored fewer away goals than any other side in English league football this season (2).
- Everton had 71% possession – their most in a Premier League game since February 2016 (76% vs West Brom).
- Since the start of last season, Gylfi Sigurdsson has scored more goals in all competitions than any other Everton player (13).
Everton go into next Sunday's derby at Anfield in fine form, while Cardiff are under pressure going into their home game against Wolves on Friday. That game is followed by matches with West Ham, Southampton, Watford and Crystal Palace – a run of fixtures that could ultimately prove pivotal in their bid for survival.