The home side's first-half dominance was rewarded in added time when the January acquisition from Sunderland clipped Tommy Smith's clever through ball past former Bluebird Tom Heaton.
And 12 minutes into the second half Campbell scored his third for the club, more than he managed in the whole of last season for Sunderland, after a mammoth long throw from Aron Gunnarsson.
A bizarre own goal from Ben Nugent reduced the deficit in added time but it was too little too late for the struggling Robins.
Campbell, who joined the club for £650,000 from the Black Cats just a month ago, immediately looked sharp in an impressive Bluebirds side.
Craig Bellamy, Craig Noone and Nugent all threatened Heaton's goal for Cardiff early on, with Bellamy notably testing the stopper from 35 yards with a free-kick.
Noone, back in the Cardiff side for the first time in a month, was the architect of the first chance, but Mark Hudson looked surprised to see his cross fall into his path and could only tap it into the arms of Heaton.
On his return to the Cardiff City Stadium, Heaton was certainly being kept busy. Seven minutes before the break he had to race out of his goal to nod Noone's lofted pass out of the path of Bellamy before showing good hands to hold Peter Whittingham's effort.
Bristol City, languishing second-bottom with just 31 points from as many games, were always second best as visitors, with Cardiff in danger of cruising to victory.
Robins striker Jon Stead flashed a handful of attempts at Ben Marshall's goal, but it was to no avail as Cardiff's continued pressure eventually paid dividends.
Campbell scored his first on the stroke of half-time, trading passes with Smith before finishing with aplomb past Heaton.
From the restart Cardiff looked even more comfortable, asserting their superiority against an albeit well-organised Bristol City side who have been reinvigorated under the tutelage of new manager Sean O'Driscoll.
But for all their efforts, the visitors were undone by another goal from Campbell, who slotted home from close range in the 58th minute for his third goal in three appearances.
Nugent's comedy own goal in the final minute - cushioning a header beyond keeper Marshall - provided a brief glimpse of hope for O'Driscoll's charges, but it mattered little in the end as Cardiff marched on towards promotion and the Robins flew closer to the trapdoor.