Everton dominated a resilient and stubborn Cardiff City side, who defended resolutely for 90 minutes only to be undone by a second half Gylfi Sigurdsson tap-in.
The Toffees bossed possession early on but were sloppy in the final third, and should have taken the lead just before the break when Sigurdsson rounded Cardiff goalkeeper Neil Etheridge only to find Sol Bamba on the Cardiff goal line.
The breakthrough came when Theo Walcott was played in through the Cardiff defence and his shot was well saved by Etheridge, but parried it straight into the path of the ex-Swansea City man Sigurdsson who placed the ball into the back of the empty net.
Everton were the better side throughout and deserved the three points but Warnock will feel his side could have taken something more from a game in which they were defensively sound.
Key Talking Point
Goalscorer Sigurdsson, usually renowned for exceptional long range goals, will probably not score an easier goal in his Everton career.
Walcott did well to get past the Bluebirds' defence and hit a low shot down to Etheridge's right, the Cardiff keeper only able to parry the ball straight to the Iceland international's feet.
The hosts did have a handful of chances to increase their lead, but found Etheridge in fine form, producing some outstanding saves.
Starting XI: Pickford (6); Coleman (6), Keane (7), Mina (7), Digne (6), Andre Gomes (8*), Gueye (6), Walcott (6), Sigurdsson (7), Bernard (6); Richarlison (6)
Substitutes: Stekelenburg, Baines, Zouma (6), Tosun (6), Davies, Calvert-Lewin, Lookman (7)
Andre Gomez, on loan from Barcelona, showed glimpses of why the Catalan giants paid £33m for his services from Valencia with a composed display at Goodison Park.
After missing the beginning of the season through injury, the Portuguese has now four consecutive appearances in an Everton shirt and is looking a top talent for the Toffees.
In the first half he was the best player on the pitch, with his 31 passes with an 87% accuracy, although in the second period he was much quieter.
Worst Player - Richarlison
It was a mixed night for the Brazilian, who failed to live up to the hype surrounding his potential in this fixture. The 21-year-old was unable to add to his tally of six goals in the Premier League this season, but did look bright and lively throughout.
He showed glimpses of his talent with exceptional footwork at times but his finishing and decision making were questionable.
Key Talking Point
Where are the goals going to come from for Neil Warnock's men? The visitors started with a lone striker, Callum Paterson up front - who played for Scotland at right-back during the international break - but rarely troubled Pickford's goal.
Victor Camarasa had the best chance, firing a shot towards the Everton goal which Pickford beat away for a corner.
Arguably, the Bluebirds should have been awarded a penalty with 12 minutes to go when Seamus Coleman bowled over Gregg Cunningham in the penalty area without even touching the ball and, in all honesty, a penalty was the most likely way onto the scoresheet for the Welsh side.
It's another fixture where Cardiff have failed to score away from home, and Warnock will surely be looking at a centre forward in the January transfer window.
Starting XI: Etheridge (8); Manga (7), Morrison (7), Bamba (7), Ralls (6); Gunnarsson (6), Arter (7), Harris (6), Camarasa (7), Cunningham (6); Paterson (7)
Substitutes: Smithies, Peltier, Bennett, Ward (6), Murphy (7), Reid, Hoilett (6)
Etheridge produced some fine saves to keep Cardiff's deficit to just one goal, but was a little silly for getting booked for time-wasting in the first half.
The keeper was unlucky that his save from Walcott's initial strike fell straight to the feet of Sigurdsson for an easy tap-in.
Rarely troubled in the first period, he was the much busier goalkeeper in the second period and gave the Bluebirds a glimmer of hope for an equaliser.
No one in the Cardiff team played particularly poorly but it was a quiet game for Aron Gunnarsson, who is usually so instrumental in the middle of the park.
He did provide the dangerous long throw-in which worried the Everton defence at times, but this was all the Icelander could really provide in a Cardiff City shirt at Goodison Park.
Next up for the Toffees is a trip across Stanley Park to take on Merseyside rivals Liverpool at Anfieldm which should be an exciting encounter.
Cardiff host fellow top flight newcomers Wolves at the Cardiff City Stadium looking to bounce back and out of the Premier League relegation zone.