Three successive defeats had led to increased scrutiny on Silva, with Everton having had to wait 17 days to try and bounce back from the loss at Watford, but former Swansea City star Sigurdsson stepped up to the mark.
Having opened the scoring four minutes before half-time, Sigurdsson curled in a superb second to ensure Everton's dismal run came to an end – becoming the Toffees' leading scorer in the process.
Things could have been different if not for some excellent defending from Lucas Digne early on, but Cardiff offered little threat as they slumped to a second straight defeat, their misery compounded by a late third from Dominic Calvert-Lewin.
Phil Jagielka almost cost Everton with an untimely slip two minutes into his first start since opening day, but Digne beat Nathaniel Mendez-Laing to Kenneth Zohore's subsequent cross.
Jagielka was involved in Everton's first chance – Theo Walcott slicing his volley wide from the defender's knockdown.
Sigurdsson made no such mistake from Everton's next opening though, side-footing home with a composed first-time finish from Seamus Coleman's cutback.
34 - Everton’s Gylfi Sigurdsson has been involved in more Premier League goals in games played in Wales than any other player (13 goals, 21 assists in 68 appearances). Dragon. pic.twitter.com/J9cKDkNxBV— OptaJoe (@OptaJoe) February 26, 2019
And Sigurdsson came up with the goods again in the 66th minute, drilling in on the rebound after Bernard's low cross was blocked.
Further gloss was added in the final minute of stoppage time, Calvert-Lewin capping his 100th appearance in league football with a well-taken goal to get Everton back on track in emphatic fashion.
What does it mean? Everton out of the woods
Everton have had a torrid run since the first Merseyside derby of the season, but Silva will now be hoping his side have put any lingering doubts over getting dragged into a relegation scrap to bed as they prepare to face Liverpool once again in their next outing.
Ex-Swan Sigurdsson back to haunt Cardiff
Sigurdsson enjoyed his time in Wales with Swansea over two spells, and made his mark against their arch rivals. His first strike brought up his 56th Premier League goal, making him the outright leading Icelandic goalscorer in the competition, ahead of Eidur Gudjohnsen.
Richarlison missing his spark
Having had a fine start to the campaign, Richarlison has faded in recent outings, and a lacklustre display – which was cut short after an hour – was made worse when his replacement Bernard played a crucial role in Everton's second.
Key Opta Facts
- Everton have done the league double over Cardiff for the first time since 1928-29.
- Cardiff have never won a midweek Premier League game (Tuesday, Wednesday, Thursday), drawing three and losing seven. They have scored just two goals in those 10 games and have conceded at least twice in each defeat.
- Cardiff are the only side to fail to direct a single shot on target in more than one home Premier League game this season, doing so against Everton and against Huddersfield in January.
- Sigurdsson has been involved in more Premier League goals in games played in Wales than any other player (35 - 14 goals, 21 assists in 68 appearances).
- Sigurdsson has scored 15 Premier League goals for Everton since the start of the 2017-18 season, five more than any other player.
Everton have the chance to help derail Liverpool's title challenge when they host their rivals in the Merseyside derby on Sunday. Cardiff travel to Wolves a day earlier.