The Scotland international registered a hat-trick of first-half assists in Merseyside to inspire her side to victory, as the visitors leapfrogged the Toffees in the table.
Weir set up Ellen White, Gemma Bonner and Janine Beckie with three excellent deliveries and Taylor hailed his midfielder’s resilience to have responded to a setback on international duty with such an impressive performance.
“I said to Caroline at half-time: she was class,” he praised.
“She showed her class with her ability, like picking out the goal for Janine. She was great.
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“She’s had a difficult period going away with Scotland. They didn’t qualify but to come back and produce that performance shows what she’s about.”
The triumph lifted City to fourth in the table – five points behind league leaders United – and marked the perfect start to December: a crunch month with three must-win league games and the return of the Champions League.
Taylor hopes the manner of victory at Walton Hall Park can provide a major boost ahead of the coming weeks.
“It was a tough game. It always is against Everton – they don’t give up,” he reflected.
“We went in 3-0 at half-time but it was wasn't easy in the second half – they made is difficult and we made it difficult for ourselves sometimes.
“We have to be happy with three points, a clean sheet, some good performances and some really good goals.
“The important thing was to get three points on board to keep right in amongst it
“Games are coming thick and fast. It’s great.
“We’ll focus on Europe and then before you know it, it’s straight back to the WSL at the weekend.”
There was further cause for celebration as Lauren Hemp returned from injury for her first minutes since August’s Community Shield.
Taylor expressed his delight for the PFA Young Player of the Year's return but also shared disappointing news on Rose Lavelle, who was substituted at half-time due to injury.
“It’s great for Lauren (to have come back),” he added.
“She’s worked tremendously hard. It’s a big impact. She’s a top player and to not have had her for the first part (of the season) has been a big loss for me and for the team.
“To have her back is great. It’s a case of making sure we’re giving her the right minutes to get her up to speed to be really ready.
“It’s a shame for Rose because I thought she did really well in the game. She looked bright, worked hard and created things for us.
“It looks like one we’ll have to assess. We’re a little bit in the dark at the moment but hopefully, it’s not too bad because she’s a really good player for us to have.”
Match highlights from Walton Hall Park and a full 90-minute replay of the match (available with a CITY+ subscription) will be available from noon UK time on Monday 7 December.