Fisayo Dele-Bashiru put the Blues on their way early in the second half and sub Jayden Braaf scored twice in the last 13 minutes to cap a welcome win for Paul Harsley’s side.
City looked anything but second bottom of the Premier League 2 table as they set about their task at a damp and chilly County Ground.
The Blues slick passing had Rovers in trouble early on with Morgan Rogers causing the home defence concern with his powerful surging runs down the left.
Despite the impressive start, a cross into the City box on eight minutes saw Taylor Harwood-Bellis almost direct the ball into his own net, but he quickly recovered to clear off the line.
On 17 minutes, City came within inches of taking the lead as skipper Tommy Doyle found himself in space 15 yards out, but his curling effort went agonisingly wide.
Rovers offered little in the way of a threat and the next opportunity again came City’s way when excellent work from Ian Poveda-Ocampo gave Fisayo Dele-Bashiru time to spin off his marker and fire a low shot in that Joe Hilton saved with his feet.
And Dele-Bashiru was involved in the last chance of the first after his burst into the box and reverse pass was fired over by Rogers.
With the inspirational Doyle driving the Blues forward, City finally went ahead on 56 minutes.
Rowan McDonald played a peach of a pass from 10 yards inside his own half and Dele-Bashiru controlled the ball on the side of the foot before slotting home from close range.
Three minutes later Doyle sent Poveda-Ocampo clear, but Hilton again saved well with his feet.
In a feisty Lancashire derby there were several heated exchanges between the two sets of players as tempers threatened to boil over.
City’s dominance was rewarded when sub Jayden Braaf drove at the Rovers defence, Doyle’s clever run opened up space and the silky winger hit a low shot into the bottom corner from 20 yards.
And Braaf had the last word the classy Dutch teenager bagged a second to cap a wonderful 20-minute cameo as Rovers keeper Joe Hilton and defender Lewis Thompson collided and the ball ran free to Braaf who rolled the ball into the empty net.
Star man: Tommy Doyle
The young EDS skipper gets better and better and his tireless work was at the heart of everything good City did.
What it means…
City should move up a place to tenth in the table and Harsley will look to build on this confident performance in the coming weeks.
Tommy Doyle: "I think it’s not been easy, and we have kind of played like this on other occasions, but it’s about finishing your chances and being clinical and that’s what we were tonight.
"When we put our opportunities away, you can see, we are a top side and hopefully that’s the marker we’ve set, and we can kick on from here.
"In these types of games, it’s important that the players who have had the experience of first team football and have the confidence to go out and show it – there were 11 men tonight who took the game by the scruff of the neck and played really well as a team."
City take on Shakhtar Donetsk in the UEFA Youth League on Tuesday afternoon needing a victory.
Then it's off to Shrewsbury Town in the Leasing.com Trophy a week on Tuesday.