Winning eight league titles and the Champions League was, it transpires, the easy part. Keeping Cardiff in the top flight could be Ole Gunnar Solskjaer's greatest achievement. "It would rank as the highest," said the Norwegian, before stating with absolute certainty: "And it will. The bulk of my career has been winning trophies, yes, but you can look and say 'what is success for Cardiff this year?' It is staying up and we are so close."

Cardiff's hope must be that his confidence is infectious and justified. The bare facts are that they have lost 10 of their last 14 league games and won only two. They have not taken a point on their travels for three months. They are the Premier League's second lowest scorers and only Fulham have conceded more goals. Given their inferior goal difference, they are in effect four points – rather than three – from getting out of the bottom three.

Yet if their manager's breezy optimism felt familiar, it was because it echoed the innate positivity his Everton counterpart used to exhibit in Wigan's annual relegation battles. Roberto Martínez and Solskjaer are kindred spirits, Anglophile imports who have replaced austere Scots and introduced a more ambitious style of play.

Now Solskjaer has a high-profile admirer. "What is significant is Cardiff's performance,"Martínez said. "I never saw a team at the bottom of the table. I saw a unit with a real togetherness, a real knowhow. Ole has brought a tactical flexibility."

It is a shared interest. Martínez used to switch between three- and four-man defences. Solskjaer started on Saturday with both a back five and a midfield diamond, changed to 4-1-4-1 and made a Martínez-esque attacking gambit when bringing on Wilfried Zaha for Fabio da Silva. Had the substitute been awarded a penalty when Sylvain Distin fouled him, Cardiff may have secured a first win at Goodison Park since 1926.

"He was fantastic when he came on," Solskjaer said. "He has something different. I thought he did enough to win the game but never got the decision."

Everton's reprieve preceded Seamus Coleman's looping, lucky winner while, some 200 miles south, Cardiff's relegation rivals West Bromwich scored a late decider at Swansea. "They might be the defining minutes," Solskjaer said.

It may be the difference between playing at Goodison Park and Griffin Park next season. Two years ago, Martínez kept Wigan up with an improbable run of seven victories in the final nine games. If Cardiff's plight is not quite as desperate, Solskjaer admitted: "We definitely need heroes now."

Everton have a habit of finding them, especially when they are drawing in the final few minutes of games at Goodison. Coleman was the latest to oblige, slicing in his sixth goal of the season. "It is quite difficult to find a better full-back than him," said Martínez. Coleman's capacity to arrive in the 18-yard box belies the job description. The all-action Irishman is more the Irish Cafu than the new Tony Hibbert but the scuffed finish, which also brought him a goal against Stoke, is becoming his party trick.

Man of the match David Marshall (Cardiff City)