The Blues, who beat West Ham 5-1 last weekend and Everton 4-1 in midweek, had to be patient against the struggling Robins and with an hour gone, only had Tessa Wullaert's first-half goal to show for almost complete dominance of the game.
But Ellen White doubled the advantage on 65 minutes and City added a late flurry of goals with three in the final eight minutes - two for sub Pauline Bremer and a long-range effort from Caroline Weir.
City and Bristol came into the game on the back of contrasting fortunes.
The Blues thrashed Everton 4-1 in the Continental Cup in midweek while Bristol lost 7-0 against Arsenal in the same competition.
City were looking to make it four wins on the bounce in all competitions and began stroking the ball around nicely while Bristol defended in numbers.
The first real opportunity came when Tessa Wullaert picked out Ellen White with an inviting cross on 16 minutes, but the ball just evaded the England striker’s diving header attempt.
Janine Beckie, revelling in her right wing-back role, was a constant threat to the home defence and it was no surprise when she created the opening goal of the game.
Beckie’s deep cross found Wullaert in the box and the Belgian had time to control the ball before placing a low shot wide of the keeper for her third goal in three games with 21 minutes played.
City almost added a second just before the break following a wonderful team move that ended with Beckie’s hard low cross just missing the boot of White.
City continued to dominate after the restart, but a swift counter-attack saw Ebony Salmon force a good save down to her left by Ellie Roebuck.
And from the resulting corner Jas Matthews missed a header from just a couple of yards out to remind the Blues there was still work to be done in this game.
City gradually resumed control and after a couple of half-chances, Keira Walsh threaded a defence-splitting pass into the path of Ellen White who hit a low drive through the keepers legs to double the Blues' lead on 65 minutes.
The Robins came close to pulling a goal back when the dangerous Salmon fired a shot in from 20 yards that Roebuck did well to push away.
However, City made it three on 84 minutes with two of Nick Cushing's subs combing to give the score a more realistic look.
After neat build up on the left, Georgia Stanway played a short pass across the box to Pauline Bremer and the German span and hit a low shot into the bottom corner to seal the points.
City added a fourth goal in the dying moments with Caroline Weir hitting a trademark long range effort from 22 yards that nestled in the bottom left-hand corner as the hosts tired.
And the same pair who made the third goal combined again in added time with Stanway assisting another clinical finish from Bremer.
What it means…
City replace Chelsea at the top of the table - at least for a few hours with Chelsea's clash at Birmingham starting later in the day.
The Blues' goal difference could yet prove crucial and is markedly better than both Chelsea and Arsenal at this stage.
Star player: Janine Beckie
The Canadian set up the first goal and almost claimed a couple more assists in an all-action performance.
Keira Walsh was excellent throughout and both Georgia Stanway and Pauline Bremer gave impressive cameos.
City take on bottom club Liverpool at the Academy Stadium next Sunday (December 1) at 2pm in the FA Women’s Super League.
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