The winger's close range header secured all three points after Simone Magill cancelled out Izzy Christiansen's first half opener, to send City top of the group after two games.
There was more reason for the Blues to celebrate as Karen Bardsley made her return from injury, though she was rarely called upon as the home side dominated the opening period.
Christiansen had already tested the palms of Everton ‘keeper Kirsty Levell when Parris latched onto Claire Emslie’s lofted through ball in the ninth minute.
The winger was clear of the Toffees' defence but shot wide of the left-hand post from 10 yards.
Parris thought she’d opened the scoring moments later as her low effort rolled into the back of the net, but, after much deliberation, the referee ruled it out for offside.
Nick Cushing’s side were in control, with Bardsley only called upon once, dealing with Claudia Walker’s speculative effort with consummate ease.
A succession of corners troubled the visitors and might have brought a goal but that crucial final touch eluded City.
However, with Parris and Emslie providing a constant outlet down the flanks it was only a matter of time before the Blues opened the scoring.
When the goal came it was thanks to an inch perfect pass from the skipper.
With Christiansen running unmarked into the six-yard box, Steph Houghton played a long ball over the top, which the midfielder duly nodded into the bottom left corner.
Everton rallied somewhat and began to restrict the home side from creating as many chances, though Jen Beattie may have done better when she headed over from Keira Walsh’s free kick just before the interval.
Immediately after the restart Jill Scott nearly doubled the lead.
Finding space on the edge of the area the England midfielder clipped the top of the crossbar with a 20-yard chip.
It proved to be a closer affair in the second half with both sides moving the ball nicely from defence to midfield, but neither were able to deliver a telling final ball.
City remained the aggressors and Parris went close to grabbing the second just after the hour mark.
Good work from Christiansen found the Liverpudlian on the right of the area, but she fired over when she had time to pick her spot.
It was Beattie’s turn next as she rose highest and look to have found the back of the net with a powerful header but Levell somehow clawed it out of the top right corner.
Bardsley had been untroubled all night, but Everton forced an equaliser thirteen minutes from time, when Magill got her head on Chloe Kelly’s free kick to turn it inside the left-hand post.
City’s response was instant.
The Toffees were indebted to Levell who kept Scott’s header out from point-blank range, but a minute later and Parris headed home a left wing centre from two yards to get the goal her performance deserved.
Not content with a one goal lead, City poured forward as the final whistle neared and Parris almost got a second when she caught Levell off her line with a 25-yard effort, but the 'keeper scrambled back to make the save.
How they lined up
Bardsley was in goal for the first time this season and she was protected by a back four of Abbie McManus, Houghton, Beattie and Demi Stokes.
Christiansen and Scott played just ahead of defensive shield, Walsh, in midfield, while Parris and Emslie operated on either flank.
Georgia Stanway led the line up front.
City travel to Norway for the first leg of the Champions League last 16 tie against LSK Kvinner on Thursday 9 November (5:30pm GMT).
Cushing's side are back at the Academy Stadium in a return to league action as they welcome Bristol City Women on Sunday 12 November (2pm GMT), while the Continental Cup campaign resumes at 2pm on Sunday 3 December, as Birmingham City Ladies visit the Academy Stadium.