The Foxes took their tally up to 16 points in the Barclays Women's Super League as Yuka Momiki, Saori Takarada, Janice Cayman, Jutta Rantala and Denny Draper all found the net in a dominant performance on Filbert Way.
Willie Kirk made three changes to the side that beat Birmingham City in the Adobe Women's FA Cup, with Sophie Howard, Missy Goodwin and Janina Leitzig - the goalkeeper missing through illness - all coming out for Aileen Whelan, Julie Thibaud and Lize Kop.
Before kick-off, there was a special moment pitchside as Club captain, Whelan, was awarded a framed shirt to mark her 150th WSL appearance.
Leicester were on top from the first whistle, setting up camp in the Bristol half, coming closest when CJ Bott pulled a low cross back to Sam Tierney inside the box, but the midfielder's curling effort was wide of the far post.
The deadlock was broken after 20 minutes, against the run of play, by Bristol City when Ffion Morgan picked up on a loose pass and found the net, but after constant pressure, City were back level.
Momiki scored her first Leicester goal in extraordinary fashion when she broke into the Robins' box, and from an tight angle, hit a left-footed strike over the top of Shae Yanez into the back of the net.
The control paid off once more, just before the break, when fellow Japanese Takarada followed up on Whelan's initial shot, giving the hosts a well-deserved lead going into half-time.
Following the restart, Bristol City showed why they were still in the game and, with Amalie Thestrup on the break, ran through on goal and placed the ball past Kop, bringing the scores back level at 2-2.
This left Leicester in the awkward position of once again chasing the lead, but having achieved this once already, they scored a third when Cayman turned a Tierney cross goalwards, beyond the reach of Yanez.
As the Robins' legs began to tire, Kirk introduced Deanne Rose and Draper into the game, the pair running riot in the final stages. There was soon a momentous occasion as the young English forward netted from close range to score her first professional goal.
Despite a couple of stressful moments caused by Bristol City's pace up front, Leicester held on for a comfortable victory on Sunday afternoon, as they remain seventh in the WSL, three points behind Tottenham Hotspur and the top six.