Cardiff City took another step towards the Premier League on an afternoon when Fraizer Campbell marked his home debut with a performance that suggests he is determined to make up for lost time. Signed for £650,000 from Sunderland last month and given his first start since the opening day of the season, Campbell scored twice to inspire the Championship leaders to a victory that was far more comfortable than the scoreline suggests.

Ben Nugent's own goal in injury time forced Cardiff to endure an anxious final few minutes, although it would have been a gross injustice if Bristol City had got anything out of this game. Malky Mackay's side dominated from the start and, but for a fine display from the former Cardiff goalkeeper Tom Heaton, the breakthrough would have come long before Campbell adroitly steered the ball home with the outside of his boot on the stroke of half-time, following Tommy Smith's perfectly weighted pass.

Campbell's second, rammed in from close range in the 58th minute after the visitors had failed to deal with Aron Gunnarsson's long throw, was no more than Cardiff deserved and took the former Manchester United striker's tally to three in three games for the Welsh club, which is more than he managed in the whole of last season. It seems odd to think that campaign included an England call-up, when Campbell came off the substitutes' bench in the 3-2 defeat against Holland 12 months ago.

While Campbell is unlikely to feature in Roy Hodgson's England plans any time soon, the 25-year-old could prove to be a valuable acquisition to a Cardiff side that has developed a reputation for picking up victories – this was their 12th win in their last 16 Championship matches and maintains their eight-point lead over second-placed Hull City – despite struggling to score goals. Heidar Helguson and Peter Whittingham, Cardiff's joint-leading scorers, have scored seven league goals this season.

Campbell will soon be closing in on that tally, assuming he stays fit, which is the one query hanging over him after spending so much time on the sidelines at Sunderland following two serious knee injuries. "I felt it was time to start him," Mackay, the Cardiff manager said. "It's about bleeding him in gently. He's not played a lot of football over the past nine months and, that being the case, we have to make sure we treat him properly in terms of getting him up to match fitness.

"I don't doubt the quality of the footballer we've got. You could see the quality there today – the intelligence, the strength, the link-up, the pace, and obviously strikers want to score goals, so for him to get the two goals was really pleasing for him. But more than anything I'm delighted about the lack of ego of the boy and the way he's thrown himself into the way I want to work here. He's bought into that and grasped it."

Campbell departed to a standing ovation in the 73rd minute and by that point it was hard to see any way back for a Bristol City side that had threatened only sporadically. Jon Stead squandered a reasonable chance early on when he volleyed a flighted pass from Steven Davies over the crossbar but that was a rare attack from the visitors during an opening 45 minutes when Heaton made decent saves to deny Craig Noone, Craig Bellamy and Campbell.

A fourth successive away defeat for City leaves Sean O'Driscoll's side in the relegation zone and suggests that it will be their form at Ashton Gate over the remainder of the season that determines their fate. "We get a goal back at the death and if we hadn't conceded a poor second goal we could have walked away with a point, which would have been pleasing," he said. "But we weren't effective enough with our limited possession."