He latched on to a ball from Rowan Vine in the 18th minute to rifle home from close range and then repeated the dose five minutes before the interval.
Wayne Routledge switched play to the right to wrongfoot the home defence and Simpson raced in unmarked to shoot across David Marshall and into the far corner.
Magilton said: "We executed our plans to perfection which rarely happens although it helped that we never had a midweek match while I saw Cardiff go down to 10 men in their game and forced to work very hard in their match against Reading.
"Some of our play today was excellent, we were clinical and Jay Simpson scored two good goals to earn just reward for a great performance.
"I don't want to get too carried away but to come to Cardiff and win in such a manner was very pleasing.
"This is a difficult division to get out of and I am no different to all the other managers who believe they can make an impact."
Cardiff rarely played like a side challenging at the top and Michael Chopra and Jay Bothroyd rarely had a shot on goal.
If Vine had found the net on the hour instead of hitting the far post the result would have been much worse for Dave Jones' side.
"We never got going and looked slow and lack lustre," said Jones.
"When it is going wrong you have to stick at it and it took an 18-year-old in Josh Magennis to show the rest of the players the way.
"Perhaps some of them thought they only had to turn up but football has a habit of kicking you in the teeth.
"Our forwards were non-existent although Chris Burke did try but there were some who failed to put a decent shift in.
"I will forgive the players if their passing is off but I can't defend them for that performance because you cannot stroll around the pitch and all the hard work in midweek has been lost.
"The opening goal is always important and their first was offside but we shouldn't have stood still trying to play it.
"We never worked hard enough today and that is what has let us down."