Chelsea took advantage of Scott's dismissal just after the hour mark, with Bright striking in a thunderous opener from 30 yards, four minutes after the red card, before Cuthbert added a second in stoppage time.
CITY+ | Sign up for exclusive content
188 days after their thrilling 3-3 draw in the WSL, the two sides met for the 11th time since January 2018, making history by participating in the first FA Women's Community Shield at Wembley Stadium.
City started on the front foot and won a corner inside 15 seconds, however, the first big chance of the game fell to Hayes' Chelsea in the third minute.
Ji So-Yun accurately played through Kerr, but with only Ellie Roebuck to beat, she fired into the side netting - a huge let-off for City.
Taylor's side settled down after the early scare and dominated possession of the ball, with our first meaningful effort coming after 22 minutes.
Lauren Hemp dribbled her way into the box and Chelsea's scrambled clearance fell to Georgia Stanway, who struck a sweet half-volley from 20 yards, but shot-stopper Ann-Katrin Berger leapt to her right to stop the ball nestling into the top corner.
Then, seconds before the half-hour mark, City substitute Beckie had the ball in the net just three minutes after being introduced - only for it to be ruled out for offside.
The lively City debutant Kelly superbly tricked her way past three Chelsea defenders and squared for Beckie to tap in from close range, but the offside flag was rightly waved.
Three minutes later, it was Chelsea's turn to come close to the opener. Ji's deflected free kick landed at the head of Kerr six yards out, but she directed her header wide of Roebuck's post.
It became end to end stuff at Wembley, with Berger parrying Stanway's low effort into the path of the onrushing Kelly, whose strike cannoned back off the post ten minutes before the interval.
Chelsea emerged from the break on the front foot and in similar fashion to the first period, should have taken the lead three minutes into the second half.
Fran Kirby raced down the right flank and delivered a perfect cross for the unmarked Kerr, who scuffed her effort wide from six yards out. Another big let off.
On the hour mark, we created our best chance of the afternoon. Scott threaded the ball through to Stanway who raced through on goal but fired wide of the right post with her weaker left foot.
Seconds later, Kerr spurned another fantastic chance for Chelsea, poking wide with only Roebuck to beat after referee Rebecca Welch played an advantage for Scott's foul on Ji.
Welch came back to the incident, showing Scott her second yellow card of the match, reducing City to ten with 28 minutes remaining.
Four minutes later, our resistance was broken by a thunderous 30-yard strike from Chelsea centre-back Bright, with the ball dipping beyond Roebuck.
Ten-woman City were firmly on the back foot and almost fell two goals behind three minutes after the opener, but Melanie Leupolz blasted over the crossbar from eight yards out.
The London side added a second in stoppage time, with Cuthbert blasting into the top corner from ten yards out to seal the victory.
What it means
City miss out on the first piece of silverware of the new season, with Taylor losing his first competitive match in charge of the team.
Player of the match
Chloe Kelly. The City debutant was a constant threat to the Chelsea backline, completing some dazzling dribbles and oozing confidence with the ball.
The youngster struck the post in the first half and almost provided one of the best assists in recent years.
How we lined up
Gareth Taylor’s side begin their 2020/21 FA Women’s Super League campaign a week from today, travelling to face Aston Villa on Saturday 5th September, with kick-off scheduled for 14:30 BST.