Shaw scored her eighth goal in seven Women's Super League games as Manchester City beatEverton
Shaw picked up a looped ball from Ouahabi as Ramsey came out of her goal to meet Shaw, leaving an empty net for the Jamaican to square the ball to Blakstad who scored.
Sandy MacIver tried to punch the ball away from a corner, but it fell to Rikke Sevecke who headed into the back of the net.
Shaw tapped in the rebound after Laura Coombs' shot went off the post and into the net.
City's fifth consecutive victory in the Women's Super League, despite being without injured winger Lauren Hemp, moves them fourth, level with Manchester United in third place.
The loss was their third in a row at home and leaves them in seventh place.
Saturday's late kick-off is when Manchester United will play their first game at the new stadium.
Replacing Ellen White, who retired after the summer Euros, as the starting number nine at City is no mean feat but Shaw has taken on with ease.
She scored her eighth goal of the season, the most in the WSL, and wreaked havoc on the team.
City would have preferred a role reversal as four of Shaw's goals this season have come from heads.
Shaw's shot from near the byeline found the back of the net, but she was ruled to have been in an area where she shouldn't have been.
After back-to-back losses at the start of the season, City have won their past five games in a row, their best run since the start of the season.
Kelly tried an overhead kick which was helped along by Blakstad, but her head hit the post.
They seem to be clicking with a strong starting line-up and options on the bench compared to last season when they struggled for depth because of injuries.
It is the best 100% record one team has against another in the competition.
When the first goal is scored, the Toffees have not won a game.
They had chances to get something from the match and the additions of Beever-Jones and Gio made an impact late on.
When Beever-Jones smashed a shot into the side-netting, after Ouahabi blocked a shot by Gio, the two sides had just one goal left to play.
After Beever-Jones had another chance to level but her shot was weak, Ramsey was called upon to save a Kelly shot that was headed for the top corner.
Jess Park, who scored on her England debut last week, was unable to play against her parent club, so they were missing a moment of brilliance.