Willie Kirk's visitors almost opened the scoring in the seventh minute when Hayley Raso delivered an inch-perfect cross to Valerie Gauvin, whose flicked effort was superbly blocked on the line by Ann-Katrin Berger.
The Toffees had another glorious opportunity when the ball fell to Claire Emslie and she struck a powerful volley that forced Berger into a smart save.
Seven minutes later, Bethany England tried her luck with an audacious and curling effort from long range but the ball came back off the woodwork.
However, Emma Hayes' side did break the deadlock in the 28th minute. Kerr took advantage of Everton's sloppiness and squared the ball to Reiten to fire a left-footed strike into the bottom corner.
The second half saw a more positive start from Chelsea and Millie Bright lashed a speculator effort against the crossbar.
At the other end, Izzy Christiansen looped a dangerous cross into the penalty area and Berger tipped the ball over the bar.
In the 77th minute, Chelsea doubled their advantage as Kerr fought hard to win the ball and drilled a powerful effort past Sandy MacIver.
The Blues sealed their place in the last eight of the competition after Kerr found substitute Spence, whose header was deflected in off the far post.
- Emma Hayes' thoughts
Guro Reiten opened the scoring in the first half before goals from Sam Kerr and Drew Spence after the break secured Chelsea’s place in the last eight, which will not take place until September.
The result came on the back of last Sunday’s 4-0 defeat to Barcelona.
“There is no real shame to have a silver medal from a Champions League final,” said Hayes.
“It’s a beautiful medal and it’s a stark reminder that from going silver to gold we had to find something else within our group, so that’s a challenge.
“Tonight’s line-up clearly showed why my job is so difficult because everyone is good enough to start.
“To compete in the Champions League we need the squad depth and every week we have some disappointed faces. It’s not an easy task every week.
“When we came into the game tonight, I wanted to see Chelsea Women at its best and, whoever I pick, I can get a strong performance from every player.
“It is a real fabulous achievement from the players, they deserve every bit of credit that they’ve gained this year.”
- Willie Kirk's thoughts
Everton manager Willie Kirk was left disappointed by his side’s performance, having made a dominant start to the game.
The visitors could not replicate the victory they produced against the same opponents in last season’s quarter-finals, when they triumphed 2-1 before eventually losing to Manchester City in the final.
Kirk said: “We were looking very threatening at times and had some great spells. It probably sums up our season and what we are lacking.
“That has happened to us in the past. We either conceded two goals really quickly or we’ve been on top, built our confidence up in terms of our possession, then we get switched off and get punished.
“We created an awful lot of chances. I think we took the game to Chelsea and the result simply summarised our season.
“For spells of games, we can without doubt compete against the top teams. It’s just over 90 minutes, the game management and managing the big moments is where we need to develop moving forward.
“Next year, I think we will see some improvements.”