Report from the BBC
The Bluebirds went ahead eight minutes before the break when Hayden Mullins turned the ball into his own net.
Bothroyd added their second after capitalising on a mix-up between keeper Jamie Ashdown and Ibrahima Sonko.
Portsmouth had chances through captain Marc Wilson and David Nugent, but Cardiff keeper David Marshall saved both efforts.
The Bluebirds remain second in the table, but are now level on 10 points with leaders Queens Park Rangers, while cash-strapped Pompey are bottom, with just one point from four games.
It was sweet revenge for Cardiff boss Dave Jones in the first meeting between the two sides since Portsmouth beat Cardiff 1-0 in the 2008 FA Cup final at Wembley.
Both clubs have since suffered much-publicised financial problems, necessitating a number of visits to the High Court.
But Pompey's problems have been far greater, as was evident to see in the form of the ex-Premier League side's threadbare squad.
Cardiff appear to be turning a corner, and the capture of Craig Bellamy on loan from Manchester City is a sign that the new Malaysian investors mean business.
The visitors deservedly came away with the points, with the goals typifying Portsmouth's struggles.
Both sides took their time to get going though, with Pompey striker John Utaka looking the most useful in the early stages.
But it was captain Marc Wilson, widely tipped for a move away from Fratton Park, who had the first chance on 12 minutes.
That came after Bothroyd clumsily bundled Carl Dickinson, and Wilson drilled the resulting 30-yard free-kick towards goal, forcing Marshall pushed over the bar.
Two minutes later, it was the turn of the home side to defend as Cardiff looked dangerous on the attack.
Chris Burke made a brilliant run down the right before cutting inside and laying off to the onrushing Bellamy, who curled right-footed just around the far post.
It spurred on the visitors, and they should have done better, but didn't have players in the right places when Pompey twice failed to clear their lines.
Keeper Ashdown was called upon to make his first save on the half-hour when he had to turn away Burke's cross-cum-shot at the near post.
It was still a pretty even contest and with 10 minutes to go before the break, Wilson chipped a long free-kick into the box which Sonko headed just over from six yards.
But Stoke-target Wilson, who had done little wrong in the first half, was caught out two minutes later, which led to Cardiff's first goal.
He was dispossessed in his own half by Danny Drinkwater, and the Manchester United loan signing hit a through-ball aimed for Bothroyd, which Mullins diverted into his own net.
Pompey could have made amends just before the break when Nugent was picked out in the box only to see his right-foot was brilliantly saved by Marshall.
But Cardiff showed their intent at the start of the second half and got their reward with just four minutes of it gone, moments after Mark Hudson headed just wide from a corner.
Ashdown and Sonko were guilty of messing up a straightforward clearance, allowing Bothroyd to nip in and fire into an empty net his sixth goal in as many games.
Portsmouth battled to find a way back in, but rarely looked like penetrating a stubborn Cardiff defence.
Bluebirds boss Dave Jones brought on new loan signing Andy Keogh for Bellamy in the last 10 minutes, who had the ball in the net in injury time with a header from Lee Naylor's cross, but it was ruled out for offside.