A dominant first-half performance laid the foundations for City to run out comfortable winners over relegation-threatened Gillingham.
Matt Smith struck a brace with two goals in ten minutes late in a first period in which the visitors produced some of their best football of the season.
Cody McDonald halved the deficit immediately after the break, but Scott Wagstaff wrestled the momentum back in City’s favour with a fine curling shot after 55 minutes.
From then on City were rarely troubled on the second of three separate visits to Priestfield in the space of two months.
Steve Cotterill made four changes to his side victorious over local rivals Yeovil Town on Boxing Day.
Derrick Williams returned from a one-match ban with Greg Cunningham moving to left wing-back at the expense of Joe Bryan, while Jay Emmanuel-Thomas made his first league start of the season in place of the injured Kieran Agard up front.
Elsewhere, Wagstaff and Marlon Pack were preferred to Mark Little and Todd Kane respectively, with City in action for the second time in the space of 48 hours.
It would take a dominant first-half display not dissimilar to the FA Cup meeting in November to leave the visitors firmly in control at the interval.
Having opened his City account at Ashton Gate two days prior, striker Smith was in the mood for more and found himself the target of numerous crosses right from the start.
First he attempted a difficult lob over the advancing Stuart Nelson, before heading Luke Ayling’s right-wing delivery into the arms of the Gills keeper.
But the hosts sprung into life on eight minutes with the first enterprising move of the match, culminating in Michael Doughty whipping a left-footed shot just a couple of yards wide.
However, by the quarter-hour mark City were bossing the game and enjoying sustained spells of possession, one of which ended with Emmanuel-Thomas shooting from 20 yards only to see his right-footed strike turned aside by Nelson.
Smith threatened again from headers either side of Emmanuel-Thomas seeing a goal chalked off after Cunningham was ruled offside in the build-up.
The Gills were hardly seeing the ball but did spurn a fine chance to open the scoring completely against the run of play when Danny Kedwell sent a free header wide from a left-wing corner.
Ironically it would be a corner at the other end from which the hosts were undone.
Ayling had already been denied by the foot of Nelson from one Luke Freeman set-piece, before another dead ball from the same side was headed back across goal by Aden Flint and glanced in with the slightest of touches by Smith from just a couple of yards.
It was a goal thoroughly deserved on the balance of play, and Smith would soon double his tally before the interval.
This time City would take the open play route, as Williams’ clever clipped pass around the corner set Cunningham free down the left, who waited for the bouncing ball to drop before rolling an open invitation across goal for Smith to tuck away his second from six yards.
Cotterill’s side seemed virtually home and hosed, but opposite number Peter Taylor responded with a double substitution at the break and got exactly the response he craved as McDonald halved the deficit within two minutes of the restart.
Collecting the ball just inside the City half, the striker was allowed to run unopposed to within shooting range before dispatching a low shot just inside the far post from 20 yards with Frank Fielding rooted to the spot.
Suddenly there was a very different mood around Priestfield. Having booed their team off at the break, the home fans were suddenly roaring them on, sensing an unlikely equaliser in the offing.
But the sudden influx of optimism was extinguished just as quickly as Wagstaff struck his second goal of the season at the end of an incisive breakaway.
Fielding’s quick clearance launched a counter-attack, from which Freeman carried possession deep into Gills territory before supplying Wagstaff on the right corner of the penalty area.
There seemed little danger to concern the hosts, but the wing-back stepped inside his man and struck a delightful left-footed shot which curled beyond Nelson’s right hand and inside the far post to put the visitors back in command.
From then on City were able to see out the game with relative comfort. McDonald was denied by a sprawling Fielding save having latched on to a ball in behind the defence, but it was the only time the visitors would be exposed.
Smith was hat-trick hunting at the other end, but left frustrated by crosses from Cunningham and namesake Korey which did not find their intended target.
Cotterill will be hoping for more of the same when his team return to Kent for the first leg of the Johnstone’s Paint Trophy area final in nine days’ time.