Monk, put in charge for the "foreseeable future" following Michael Laudrup's dismissal, watched Wayne Routledge give his side the lead just after the break before Nathan Dyer and Wilfried Bony completed a handsome 3-0 win.
Kenwyne Jones missed two excellent first-half chances while the superb Craig Bellamy rattled the crossbar for the visitors.
It may take time for the role to become a good fit for Monk, who, perhaps understandably, did not always look comfortable with the attention focused on him and regularly sought counsel from the likes of Alan Curtis and Pep Clotet in the dug-out.
But he will not care one jot after claiming such a valuable three points, which moved the club he has served for a decade four points clear of the relegation zone and into the top half of the Premier League table.
And ex-Swansea managers Rodgers and Martinez, now in charge of Merseyside heavyweights Liverpool and Everton, had provided Monk with astute guidance as he prepared for his first game in charge.
"I spoke to Brendan, I spoke to Roberto and I spoke to Kenny Jackett. All people who have been here," he said.
"The support I have had here has been magnificent.
"They gave me advice which I will keep to myself, but they are guys at the very top of their game and when they are giving you good advice and wishing you well and giving you little bits and bobs it can only help."
Laudrup has indicated he will take legal action against Swansea over his dismissal, while Swansea chairman Huw Jenkins stated in his programme notes that the Dane lost his job because he feared the club's principles were being eroded.
Monk was clear on what he believes Swansea's principles to be, but was keen to stress Laudrup's time in south Wales will never be forgotten.
"For me, with Michael, I have massive respect for him," he said. "You don't do something like finishing ninth and winning the first major honour in the club's history without earning massive respect and we will never forget that.
"We will always respect him and have him in our minds but in terms of the fact he has gone then I suppose we do have to move on, but we never forget people who have brought stuff to the club."
On Jenkins' comments he added: "The first principle here is hard work. That was the first words I said to the players.
"It is the only way you get where you want to get. That is the main principle we have always had here, and the style of play.
"But you have to understand it and implement it every single day and I told the players when they come into training everything else stops, it's about hard work what is going on in there.
"That's what I did this week, I did not give them time to think about what else was going on or what anyone has said. We wanted it to be quick, sharp and intense. But the players know that."
The game had been goalless at the break but Swansea led when Pablo Hernandez's pass caught Fabio out of position and Routledge slotted home.
Dyer then got away from Declan John to head in a Routledge cross, before Bony powered in his 17th goal of the season.
Cardiff, who missed the chance to record the first league double in this fixture, have now lost four of the five league games Ole Gunnar Solskjaer has taken charge of.
They remain 19th, three points adrift of safety and with an inferior goal difference to all the sides above them.
And Bluebirds boss Solskjaer admitted the defeat had been painful.
"It hurts, of course, I hate losing, especially in games like this," he said.
"As anyone with Cardiff in their heart knows, there is nothing worse than losing this game.
"Every goal there is something you can point your finger at. The first goal was disappointing as we were just a split second late in all our decisions. That sets the tone for the rest of the half."