Villa equalised through a Laia Aleixandri own goal but Mary Fowler and Jess Park ensured City left Villa Park with three points.
The win takes City up to second in the WSL, six points off leaders Chelsea, while Villa remain eighth.
Villa, who were unbeaten in four games before today under the interim management of Man City hero Shaun Goater, took the lead after just six minutes through a flowing counter-attack down the right wing. Grant turned Aleixandri with ease, before advancing into the box and powering her shot past Ayaka Yamashita.
City were sparked into life and deservedly equalised on 28 minutes when Miedema pounced on a sloppy sideways pass by Villa defender Dan Turner and swept her shot first time into the corner.
And Miedema switched on the style seven minutes later, turning on the edge of the area and curling a superb finish into the top corner.
Villa started the second half strong and equalised within a minute of the restart. They got in behind City and Kirsty Hanson's cutback was turned into her own net by the unfortunate Aleixandri.
But a topsy-turvy encounter moved back in City's favour when Fowler cut inside from the right and her left-footed shot deflected off Hanson and looped over Sabrina D'Angelo.
The win was secured midway through the second period when Park polished off a sweeping City move with a sliding close-range finish.
City's recent slump in form had left them nine points adrift of WSL leaders Chelsea. A third league loss in a row for the first time since October 2021 would have been fatal to their faint title chances.
And when they were peeled open so easily by Grant early on, manager Gareth Taylor may have even feared his 100th WSL game in charge of City would be one of his last.
He would have wondered how his injury-ravaged City side would get back into the game, with Lauren Hemp out long term and top-scorer Khadija Shaw on the bench after her own absence.
Taylor had another injury headache before kick-off, when Laura Coombs pulled up in the warm-up and had to be replaced last minute in the starting XI by Park.
But up stepped Miedema, who only returned from injury herself earlier this month, to deliver. She has scored four in her three games since returning to fitness and the City attack looks much deadlier with her present.
It is a deadly edge that City will need to maintain - and enhance - to have any chance of catching Chelsea.
These are times of change at Villa, who announced former Real Sociedad boss Natalia Arroyo as their new manager this week.
Arroyo's first game will be against Chelsea next weekend and as she was not present at Villa Park on Saturday, Goater - who scored 103 goals for City's men as a player - led Villa for the fifth and final time as interim boss against his old club.
Goater has restored confidence to Villa following their poor start under Robert de Pauw with three wins during his time in charge, and he said he wanted the job full-time before Arroyo was appointed.
But while he inspired his side to quick starts in both halves, there was little Goater could do to turn the tide against City's quality.
So Arroyo moves into the hot seat, with tasks including replacing key midfielder Kenza Dali, whose departure to San Diego Wave was confirmed early on Saturday morning.
The 33-year-old was in the stands at Villa Park and was given a warm farewell from the home crowd.