The allegedly unsinkable vessel that went down one hundred years ago this week was not even built the last time Everton beat their neighbours in a cup final or semi, so this was not exactly an unexpected result. The manner of Liverpool's win was slightly surprising, given that the much-maligned Andy Carroll had missed two or three clear chances before scoring a winning goal that was simplicity itself, but the bitter truth for Everton is that they will probably never get a better chance to break a hoodoo dating back to 1906.

Liverpool can rarely have played as badly at Wembley or any other neutral venue as they did in the first hour, yet in the end they prevailed, and by a margin that could have been greater had Maxi Rodríguez or Luis Suárez been able to accept chances in the closing seconds. Kenny Dalglish's side created more opportunities in the final few minutes than Everton had managed all match, and that was part of the story. Only once, around the hour mark, did Everton seriously threaten to increase their lead, but when Nikica Jelavic broke clear and looked around he realised his was the only blue shirt withing hailing distance, so he attempted a shot that flew harmlessly over the bar. A few minutes later Sylvain Distin presented Suárez with his opportunity, and suddenly Liverpool had their game face on. Everton never got a look in again.

"We knew they would come at us in the second half, but I actually thought we had weathered that after an hour," David Moyes said. "We made a mistake and it handed Liverpool all the impetus, just when it looked as though we were frustrating them ." That sentiment will in turn frustrate Everton supporters, because whether intentionally or otherwise, Moyes's players performed too conservatively to take advantage of a Liverpool side who spent the first half playing like strangers. Not only was there too little support for Jelavic near goal, Everton's big-game players – Tim Cahill, Marouane Fellaini and Leighton Baines – were all quiet.

Moyes could have done without that, especially after claiming the whole country wanted Everton to win. Jamie Carragher made a point of mentioning that afterwards, as if the Everton manager's impudence had galvanised Liverpool. That wasn't the case, it was Distin's underhit back pass that brought Everton's opponents back to life, though once Liverpool gatecrashed the party there was an inevitability about the sub-plot subtly changing. If Moyes had slightly overestimated his side's ability to compete, several of the Liverpool players whose ability has been questioned all season came to the fore to justify their manager's faith in them.

This has not been an easy week for Dalglish, after all, with the oddly timed dismissal of Damien Comolli, but in addition to claiming full responsibility for all last summer's signings when he could easily have deflected some of the blame, the Liverpool manager boldly put Stewart Downing, Jordan Henderson and Andy Carroll on the team sheet. The decision did not look too promising in the first half, when Suárez and Carroll were getting in each other's way and Downing and Henderson were swapping flanks without managing to bother the Everton full-backs, indeed it did not look as if it would pay dividends at the start of the second half when Downing finally pinged over a decent cross only for Carroll to miss the target from the six-yard line. Neither Henderson nor Downing made it to the end of the match, though crucially Carroll remained on the field, and with Dalglish introducing first Maxi Rodríguez then Craig Bellamy just as their opponents were beginning to flag Everton must have felt they were playing a different team in the final quarter.

Perhaps that explained why Seamus Coleman launched into a stupid foul tackle on Steven Gerrard that could have earned him a second yellow card and dismissal – "a poor decision", Moyes called it – to concede the free‑kick that Bellamy calmly popped on to Carroll's head for the winner. Scoring the decisive goal in a Wembley semi-final does not turn the £35m centre-forward into a success overnight – he will be lucky to meet a defence as generous as Everton's in the final – though it buys a little breathing space and will not do his confidence any harm. Opinion is still divided on whether Carroll will ever justify the size of his transfer fee - Dalglish says he will, everyone else thinks he won't - but there was no point discussing such matters with anyone wearing red at Wembley. If you are a Liverpool centre-forward and you score the winner against Everton three minutes from the end at Wembley, you are a success, no question. Carragher might have been slightly overstating the case when he said that goal alone was worth £35m, but you knew what he meant.

Carroll now fits into a century‑long tradition of Liverpool winning against Everton when it matters. The losers can say what they like about his performances against other clubs, but in the final analysis the big fella nodded one in on a day when Everton failed even to put Liverpool's third-choice goalkeeper to the test. "I didn't have a lot to do," Brad Jones admitted. True enough. Liverpool recovered from a bad start and managed to impose themselves on the game before the end. Everton will have to reflect that by the time you get to the last four of a competition, merely containing opponents is never going to be enough.