And within two-and-a-half minutes of Bothroyd's third goal in as many games, Cardiff were level.
Chopra added a second after Bothroyd and Craig Bellamy combined, before Bothroyd turned home a free-kick.
And Bluebirds boss Dave Jones has injury concerns over captain Joe Ledley and striker Jay Bothroyd.
Bothroyd stepped over Bellamy's low cross from the left to allow Whittingham through on goal.
But Bothroyd says that no player can expect a starting spot in any competitive team.
Before Bothroyd's 77th-minute goal, Michael Chopra spurned a fine chance to get Cardiff back on level terms.
The visitors were rampant inside the opening stages, with Kevin McNaughton and Bothroyd both going close from distance.
Bothroyd and Hogan Ephraim sent shots over the bar and Taarabt was then at the centre of controversy.
Cardiff striker Jay Bothroyd had the ball in the net after 15 minutes only to see the flag raised for offside.
After a melee in the Wednesday area, the ball broke to Bothroyd on the edge of the box.
But Bothroyd hit the net after Chris Burke's late run down the left.
Bothroyd headed his second on the hour from a dangerous Chris Burke cross.
Peter Ramage denied Ross McCormack before Peter Whittingham sliced Bothroyd's downward header wide.
Jay Bothroyd hit the first of his two goals on two minutes, slamming home after Michael Chopra's shot was saved.
Striker Jay Bothroyd is also among those expected to rekindle interest from top-flight clubs after the Bluebirds' hopes were dashed.
There has been speculation over manager Dave Jones' future as well as leading players such as Joe Ledley and Jay Bothroyd.
Bellamy this time claimed the assist, whipping over a free-kick which Bothroyd headed downward and into the net from 12 yards.
Jay Bothroyd helped on a long ball into the home penalty area and Burke found the top-right corner from six yards.
The new Cardiff captain had a hand in Jay Bothroyd's first-half opener as the ball fell kindly for the big striker.
Cardiff drew level with goals in quick succession from striker Jay Bothroyd and an excellent Mark Hudson header at the far post.
Bothroyd, this week named in Capello's provisional party for the game at Wembley Stadium, is gunning for his first senior international call-up.
They have people like Chopra and Peter Whittingham, as well as Ross McCormack and Jay Bothroyd, so they are a real threat at that level.
Bothroyd is out after being booked for the fifth time this season.
The home side's luck worsened when Wolves old boy Jay Bothroyd limped off after pulling up with a hamstring injury on 10 minutes.
However, the ball ricocheted off unfortunate Doncaster defender Wayne Thomas straight into Bothroyd's path, who kept his composure well to slot past Sullivan.
Chopra, 24, is back at the Bluebirds until January to help plug the gaps created by injuries to Jay Bothroyd and Ross McCormack.
Bothroyd grabbed Cardiff's equaliser at Reading midweek to rescue a point and will again spearhead the Bluebirds for Saturday's trip to Scunthorpe United.
While Bothroyd's knee injury looks more serious as he was forced off half way through the first half to be replaced by Ross McCormack.
Wales midfielder Ledley hobbled off with an ankle injury in Cardiff's 2-0 friendly defeat to Valencia on Saturday while Bothroyd suffered a knee injury.
Between them, McCormack and Bothroyd have scored 14 of the Bluebirds' 19 league goals this season, helping to lift Cardiff to sixth in the Championship.
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