• Huw Jenkins may have unearthed another gem • 'I can see bits of Martínez and Rodgers in what he's doing'

One swallow may not make a summer but one Swan has ruined the Bluebirds' winter. Only the second Welsh derby in Premier League history gave Garry Monk a memorable flying start as Swansea's new manager and left their arch rivals even deeper in the relegation mire.

Monk, the reserve centre-half, was an eyebrow-raising choice to replace Michael Laudrup at the Liberty Stadium, but nobody was questioning the wisdom of such a low-key appointment after a 3-0 drubbing of Cardiff gave Swansea local bragging rights and, more importantly, elevated them to 10th place in the table.

Conventional wisdom held the two teams to be so evenly matched that there would only be one goal in it either way. Instead the Swans romped to victory with three second-half goals and a rousing performance that made a nonsense of their previous 10 league games, of which they won one and lost six.

The shocking poverty of their play in the 2-0 defeat against West Ham a week earlier convinced the board that Laudrup had to go and the chairman, Huw Jenkins, surprised many by his choice of Monk, 35 next month, who was finishing his playing career in the reserves with a view to moving into coaching next season.

If the appointment proves to be inspired we should not be surprised. Jenkins' record suggests he is possibly the shrewdest headhunter in the game, having plucked Roberto Martínez and Brendan Rodgers from relative obscurity with great success before winning the Capital One Cup last season with Laudrup.

Monk's triumphant start was a case of going back to the future. Laudrup's laid-back, laissez-faire methods were no longer working, so his successor took advice from, and embraced the more intense modus operandi of, Martínez and Rodgers. The result was a chalk and cheese improvement which saw the dismantling of Cardiff's dodgy defence by Wayne Routledge.

The clever winger embarrassed Fábio da Silva, who had to be substituted, racing inside the full-back to score the first goal, then providing the cross for Nathan Dyer, the smallest player on the pitch, to make it 2-0 with a stooping header. Cardiff's humiliation was completed when Wilfried Bony rose above the hapless Ben Turner to nod home a Pablo Hernández free-kick.

How had Monk brought about such a dramatic transformation in a team that had previously taken six points from a possible 30? Ashley Williams, his captain, friend and erstwhile partner in central defence, put it thus: "I can see bits of Brendan and bits of Roberto in what he is doing. He has put on their training sessions – ones we have done before and really good ones that I enjoy. Having done them himself, he knows that the players enjoy them.

"He also gave us a bit of homework, which helped a bit. We were all given a video of a BBC programme called The Fall and Rise of Swansea City to take home and watch. I've been here six years and I found out stuff I didn't know. It helped you to respect the club a bit more, which is important. Garry has been here so long [10 years] and three of us – him, me and Leon Britton – feel we have built up the club to this level and we don't want to see it go down again.

"If it happens, it's our fault. We knew that if we pulled our socks up we could get ourselves out of trouble. The players are responsible, 100%. We might look at the manager or his staff, but at the end of the day we are the ones on the pitch.

"There's a bit of a thank you to Michael Laudrup in this performance, at least that's how I feel. I hope he was watching. I won't say anything against Michael and the way it was, but we got stuck in a bit of a rut. It wasn't anyone's fault, it just happened. Sometimes you need a change."

If Swansea are back on track under new management, the opposite is the case at Cardiff, who have lost four of their first five Premier League matches under Ole Gunnar Solskjaer, two of them against rivals in the relegation dogfight. Doubts about the inexperienced Norwegian's suitability for the job surfaced again when, in the opinion of many supporters, he picked the wrong team, omitting Craig Noone, the penetrative winger who has been one of the club's few successes this season, and also Jordon Mutch, a powerful and talented midfielder who left Chico Flores for dead soon after he got on, much too late, as substitute.

Solskjaer preferred Kim Bo-kyung, a lightweight who was never more than a peripheral figure, and Peter Whittingham, who was hooked in the first half the previous week and was no better this time. In defence Da Silva has been a liability in each of his first two games and Turner, once ludicrously touted as an England contender, appears increasingly out of his depth in the Premier League, booting the ball straight to the opposition with hideous regularity.

"Cardiff City, going down," chortled the Liberty crowd, and it would be a brave, or foolish punter, who bets against it. They are at home to Aston Villa on Tuesday in what is surely a must-win fixture. "It will be a massive game and we will bounce back‚" Solskjaer said, but he is beginning to resemble a little boy lost, whistling in the dark.

Man of the match Wayne Routledge (Swansea City)