Pellegrini's City reign had got off to the perfect start with a 4-0 thumping of Newcastle, and they looked set to make it two wins out of two when Edin Dzeko's thumping drive put them 1-0 up early in the second half at Cardiff City Stadium.
But their resilient hosts hit back as Aron Gunnarsson tapped in from close range before Campbell lost Pablo Zabaleta twice from corners to head home and spark scenes of delirium in south Wales.
Alvaro Negredo got a goal back for City in stoppage time, and spurned a last-gasp chance to grab an equaliser, but it was not enough as Pellegrini was given a rude awakening.
In addition to Zabaleta's losing of Campbell for the striker's critical double, further scrutiny will fall on Joe Hart.
The England keeper, who gifted a goal to Scotland's James Morrison in last week's international friendly, hesitated as he tried to decide whether to come and claim the first corner, eventually failing to get any contact as the ball flew over him onto Campbell's head.
Joleon Lescott and Javi Garcia, standing in for the injured Vincent Kompany, also endured a torrid afternoon in the centre of defence.
But Pellegrini would not single out any player for criticism, in contrast to his predecessor Roberto Mancini.
He said: "I have not seen the goals yet, but defending set-pieces is the duty of all the team. Not just the goalkeepers and the defenders.
"It does not matter who is guilty with the two corners, conceding from two corners is too much, it is too important an area.
"When we scored the first goal I thought it would be easier for us as we were playing a team defending with 10 players inside their box.
"It was very difficult for us and I think while we did not do a very good match we did not play badly.
"We had the patience to try and score, we did it but it was a pity with the two corners."
His opposite number Malky Mackay was understandably delighted with his side's response after their 2-0 defeat at West Ham on the opening day.
The victory in Cardiff's first Premier League home game will live long in the memory for the Bluebirds faithful, and Mackay heaped praise on Campbell.
The Scot believes performances of this quality mean Campbell could soon be adding to his solitary England cap.
Mackay said: "I thought Fraizer Campbell gave their whole back four problems today.
"He worked hard over the summer and I now think I have a player there who has had an England cap and, over the piece, I think could force his way back into that squad if he keeps his head down and keeps working and playing like that against top, top players."