Bothroyd forced an own goal from Hayden Mullins before the interval on Saturday, and doubled the lead early in the second half thanks to some more calamitous Pompey defending.
These two sides met in the FA Cup final little more than two years ago but their paths these days appear to be heading in very different directions.
Pompey, who won that Wembley encounter, are still in administration and could name just four substitutes again while Cardiff, with loan signing Craig Bellamy running the show, are dreaming of the Premier League.
The hosts actually made a bright start and Marc Wilson, in what is expected to be his last game for the club, drilled a 10th-minute free-kick which David Marshall did well to keep out.
Moments later the hosts got their first taste of Bellamy's threat when he fed Chris Burke and then tore into the penalty area to meet the winger's cross, only to fire narrowly wide.
John Utaka, back in the Pompey attack after injury, fired a shot too high and Ibrahima Sonko headed over the crossbar.
But it was Cardiff who went ahead eight minutes before the break after Wilson uncharacteristically lost possession in the middle of the park.
Burke scampered clear and crossed into the area where the ball found its way into the net off the shin of Mullins, under pressure from Bothroyd.
Marshall preserved City's lead shortly before the break with a fine save from David Nugent's drive.
Mark Hudson headed Peter Whittingham's corner narrowly over the top at the start of the second half, but Cardiff did not have to wait long to double their advantage.
They were gifted the goal by another mix-up in the Pompey defence which left Bothroyd with an open net to tuck away his sixth goal of the season in the 49th minute.
Utaka sent a lob over the crossbar and Nugent fired wide of Marshall's goal, but in truth the hosts were rapidly running out ideas, and steam, with Cardiff cruising to victory.
They could even afford to give Bellamy an early finish, the Wales skipper receiving a standing ovation from the visiting fans with 12 minutes remaining.
Bellamy's replacement Andy Keogh thought he had marked his debut with a goal but an offside flag curtailed his celebrations.