Both sides saw chances to win the game, but strong defending and two brilliant saves from Janina Leitzig resulted in City taking a draw, and adding a seventh point to their WSL haul.
There was one change to the side that lost 5-1 to Manchester United last weekend at Leigh Sports Village, with Jess Reavill dropping to the bench to accommodate Georgia Eaton-Collins, who returned from illness.
With the January signing filling in at right-back, City started in a 4-4-1-1 with Sam Tierney starting further forward, just behind Remy Siemsen, who scored on her debut last time out.
Over the first 15 minutes, it felt quite a cagey affair, as both teams saw the fixture as an opportunity of vital points. Each side looked to control possession, with no clear-cut chances being created.
Any fortune for the Foxes was coming down the left-wing with Courtney Nevin delivering a number of dangerous crosses, however Siemsen and the frequent back-post arrival of Aileen Whelan were unable to connect with any effort.
Ten minutes from the break, Leicester had their best chance of the game so far. Brilliant work rate from Hannah Cain allowed the Welsh forward to win the ball high up the pitch and supply Siemsen, but on her weaker foot, City's No.19 failed to test Courtney Brosnan in the Everton net as the ball curled past the far post.
Over the final minutes of the first half, City continued to press high but were unable to penetrate the Everton defence. At the other end, the Toffees looked dangerous on the counter, but Leicester's backline stood firm to keep the scores level at the break.
The second half started in similar fashion to the first, with both sides looking to find a breakthrough with few chances falling for either side. The best coming for the visitors just before the hour mark.
With a golden opportunity from less than 10 yards out, City goalkeeper Leitzig pulled off a blinding save to deflect the ball over the crossbar, keeping her side firmly in the game.
Over the final 20 minutes, both clubs went full hammer in attempt to steal the points, and it looked like Everton may have been the side to do so when they forced another fantastic save from Leitzig.
In front of goal, with a second close range opportunity, Everton fans were off their seats in pre-empted celebrations, however the Bayern Munich loanee had other ideas, receiving a well-earned standing ovation from the City faithful.
In the final stages when Everton were piling on the pressure, Leicester themselves saw a chance to win it when Whelan drilled a low cross into the path of Cain, but the No.21 couldn't sort her feet out quick enough and the ball ricocheted behind for a goal kick.
The Foxes would've been dreaming of a win in front of their home crowd, but against a relentless Everton side, who also had chances to win it, a point and a clean sheet will be vital for Willie Kirk and his team, as they prepare for the business end of the season.
Major moment - Leitzig saves the day
Arguably the biggest moments of the game came when the visitors had the chance to score from close range, twice in the game. But key saves from Leitzig resulted in another clean sheet for the German, and a point for the Foxes.
Who impressed? - Ruby Mace
In a goalless draw, Leicester gained a well-earned point on Filbert Way and Ruby Mace, having arrived on loan from Manchester City in January, was key in breaking up play and disrupting Everton attacks.
Where do we stand - 12th
A home draw means the Foxes remain bottom of the standings, but move within a single point of Brighton & Hove Albion.
Coming up - Tottenham (A)
City have a quick turnaround as they travel to the capital to face Tottenham Hotspur at Brisbane Road next Wednesday, with a 7pm GMT kick-off.
The details…
City: Leitzig; Eaton-Collins, Howard, Plumptre, Nevin; Whelan (C), Green (C. Jones 71'), Mace, Cain; Tierney; Siemsen (Goodwin 65').
Subs: Lambourne, Levell, Purfield, Smith, Robinson, Reavill, Pike.