Three goals in 12 first half minutes from Vicky Losada, Janine Beckie and Khadija ‘Bunny’ Shaw put some daylight between the sides, before Steph Houghton’s sumptuous free-kick completed the scoring after the hour.
Although the scoreline suggests otherwise, City were made to work for the result, with Karima Benameur Taieb called in to action on several occasions throughout proceedings.
And Taylor was delighted with how the team handled those difficult situations at Goodison Park, as well as the manner in which we made the most of our chances.
"It was a really efficient and professional performance,” the City boss reflected.
"We were put under pressure in different spells. We managed the first part of the game really well and we scored some exceptional goals with real quality.
"When you've come away to a tough ground in Everton - a team who put us under some real pressure - you have to say: the girls were excellent.”
After making her debut in Wednesday's 1-1 draw with Real Madrid, Shaw’s first City goal capped off a hugely impressive individual performance from our centre-forward.
The Jamaican tapped home our third from close-range to open her account for the Club, and Taylor believes that goal added a real spark to her overall game.
And the City boss has now backed Shaw to go from strength to strength in the coming weeks, as she looks to build on a memorable WSL debut.
He declared: "As a former striker, I know what it's like - you want to get off on a good start.
"I saw a difference in her game after that - her confidence and hold-up play was a lot better.
"She has a proven track record - she was the top scorer in the French league, although Bordeaux weren't near the top.
"We know it's in her - she's capable. She wanted a good start but we were happy to be patient. It was an excellent pass to set up and then it was a nice, easy finish.”