Despite the win, City were dealt a blow midway through the second half, after Kelly was forced off on a stretcher after a collision with Birmingham defender Rebecca Holloway.
Victory moved City to the top of the WSL league title with one game left to play. However, our title rivals Chelsea - who we lead by a point - do have a game in hand.
City flew out of the blocks, and our fast start nearly saw Taylor's side open the scoring inside 30 seconds.
A loose ball found Kelly on the right-hand side of the box. However, her effort from 12-yards was well saved by Hannah Hampton.
Despite this, City and Kelly did not have to wait much longer for the opener as she found the net on the 10-minute mark.
A good run down the left allowed Lauren Hemp to pull the ball back for Caroline Weir in the box, whose low effort forced a save out of Hampton. However, the Blues shot-stopper couldn't keep out the second effort as Kelly pounced on the rebound and tapped in from close range for her ninth WSL goal of the season.
Kelly soon made it 10 league goals for the season as she added her second 15 minutes later.
A quick move down the left saw Hemp breakaway and cross a dangerous, low ball into the box that found its way to Kelly who stroked home from inside six yards, scoring City's 100th goal under Taylor's leadership.
As she had done all season, Kelly continued to cause problems for our opponents' defensive line as she hunted for a hat-trick.
The winger looked to add to her tally just before the break, as she cut in from the right-hand side before firing an effort from 20 yards wide of Hampton's goal.
The second half followed a similar pattern as the first, as City continued to dominate at the Academy Stadium.
After being fouled on the edge of the visitors' area, Weir tried her luck from the resulting free-kick but curled a strike just over the Birmingham bar.
As the game entered the latter stages, it was only a matter of time before we added to our lead, and City had a great opportunity to score a third from the penalty spot with 20 minutes left to play.
Kelly burst into the Birmingham box before being fouled by Holloway, giving the referee no option but to point to the spot.
Despite winning the spot-kick, there was bad news for City, as Kelly was forced off the pitch via a stretcher as a result of the tackle.
In spite of being given a golden chance for a third, the resulting penalty from Weir was well-saved by Hampton down to her right in a frustrating few minutes for Taylor's side.
Just minutes later, Weir tried to put her missed penalty behind her, as she beat two Birmingham defenders before firing an effort from 15 yards.
However, like the penalty, Hampton was once again equal to Weir, as she punched the fierce effort away from danger.
Our relentless search for a third was finally rewarded five minutes from time, as lifelong City fan Morgan bundled home a corner to make it three.
City still had time for one more and it once again came from a dangerous corner, as Janine Beckie's delivery fell to the feet of fellow sub Mewis, who found the bottom corner to cap off a superb performance from Taylor's team.
HOW WE LINED UP
CITY XI | Roebuck, Bronze, Morgan, Greenwood, Stanway, Walsh, Coombs (Mewis 78'), Weir, Hemp (Park 87'), Kelly (Beckie 72'), White (Lavelle 78').
SUBS | Benameur, Dahlkemper, Davies, Mannion.
Birmingham City XI | Hampton, Kelly, Brougham, Scott, Mace, Holloway, Murphy (Green 57'), Murray, Whip, Napier, Walker.
SUBS | Whitehouse, Sarri, Logan
PLAYER OF THE MATCH - Chloe kelly
Despite being forced off through injury, there is no doubt Kelly was the shining light in City's free-flowing attack.
The winger proved almost impossible to defend against, and was more than deserving of her two first-half goals.
In typical Chloe fashion, the winger was hungry to find the back of the net, as she made the perfect run - not once, but twice - to score both of her goals.
- Kelly's second goal was the 100th goal scored under Gareth Taylor's management.
- Esme Morgan found the net in a senior City shirt for the very first time.
- Victory extended our unbeaten WSL run to 18 games.
- Kelly's brace moved her to 10 league goals for the campaign, making her City's league top scorer so far this campaign.
WHAT IT MEANS
Victory means City move to the top of the WSL table, one point ahead of Chelsea with one game to play. However, our title rivals do have a game in hand due to their involvement in the Champions League.
Our final league game of the 2020/21 season sees City make the trip to the capital to take on West Ham United on Sunday 9 May at 14:30 (UK).
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