On the hottest day of the year so far, the high-pressing Foxes beat the Toffees thanks to first-half goals from forwards Lena Petermann and Shannon O'Brien, while a second-half strike from Sam Tierney proved the difference after a later surge from the Merseyside club.
In the blazing heat at Belvoir Drive, it was a tough test for City, taking on an Everton side who managed a mid-table finish last campaign, but from the off, it was clear that both sides were treating it as if it was competitive.
Leicester opened the scoring just five minutes in through their new No.9 Pettermann, who finished hard and low into the bottom right-hand corner of the net after high pressing from City allowed them to win the ball back in a dangerous position.
Everton posed a threat in the forward positions but the defensive backline and 'keeper Lize Kop were standing firm to cancel out any opportunities, and before the first drinks break, the Foxes saw their second chance when defender Sophie Howard tried her luck.
Just after the half-hour mark, Leicester doubled their advantage over the Toffees when, inside the box and facing away from goal, O'Brien, who spent the majority of last season on the sidelines with injury, managed to scoop the ball into the far corner.
In the final moments before the interval, City have two more chances, the best coming when Josie Green, who was displaying excellent control in the game, clipped a ball to Aileen Whelan at the back post, but the captain had more time than she realised and rushed an effort safely into the hands of the Everton shot-stopper.
The second half brought a change of formation for Willie Kirk's side, but not a change in intensity, and the pair of Jutta Rantala and Missy Goodwin, who were brought off the bench, were keen to impress, and the pair created a chance from close range for Petermann, who fired home, before seeing a flag raised for offside on the far touchline.
Not too long after, the Foxes did have their third when high pressing, once again, came to fruition as Tierney drove with the ball inside the opponent's half, noticed the goalkeeper off her line, and chipped a brilliant effort from 35 yards into the back of the net.
Everton did get one back around the hour mark, when one of the forwards fired a left-footed effort past Kop, clipping the far post on its way in, but this didn't stop the momentum that Leicester had worked hard to generate.
Towards the end of the game, valuable minutes were given to youngsters, including Simone Sherwood and Denny Draper, the latter having already scored nine goals in the opening three games of the season for the U21s Academy.
In the midday heat, and with the clock continuing to tick by, Everton scored a second, which looked a replica of their first, firing an effort to Kop's right, reducing the deficit to one, but Leicester's lead remained intact until the final whistle which concluded another promising run out for Kirk's Foxes.