The England right-back finally broke the deadlock in a pulsating contest at Leigh Sports Village when she glanced a corner past the impressive Phallon Tullis-Joyce 16 minutes from time.
Arsenal's 5-2 defeat by Aston Villa earlier on Wednesday had opened the door for the Blues to wrap up yet another league success, their eighth in 10 seasons and a first under new manager Sonia Bompastor.
With third-placed United needing points to secure Champions League qualification, it proved a tough task for a side still reeling from their European humiliation at the hands of Barcelona last weekend.
"It probably feels a bit unreal because we were not expecting Arsenal to drop points tonight, but being able to bounce back after the game on Sunday and win against a big team like United feels amazing," Bompastor told Sky Sports.
"This league is really competitive so for us to still be unbeaten is something really good. It's not easy to come as a new manager to a new country to adjust to a new league.
"Starting the season I was not expecting us to be in the position ... I knew we would have to fight until the end."
Still missing their injured Australian striker Sam Kerr, who has scored 99 goals in 128 matches since making her Chelsea debut in January 2020, a draw actually suited both sides but neither showed any intention of playing for one.
Chelsea had been slow to assert themselves but went close through Mayra Ramirez, Erin Cuthbert, Niamh Charles and Millie Bright.
Blues keeper Hannah Hampton produced a good save to prevent Melvine Malard giving United the lead and Grace Clinton's effort on the rebound was also blocked.
The hosts appealed unsuccessfully for a penalty after Bright clashed with Clinton but carried their momentum into the second half, with Malard and Celin Bizet bringing further saves from Hampton.
In the end it fell to veteran Bronze, a previous title-winner with Manchester City and Liverpool, to finish the job on 74 minutes and hand Bompastor's side an unassailable nine-point lead at the top with two games to play.
"We obviously knew a draw was good enough ... It makes it feel a lot better to celebrate being champions when you win a game," Bronze told Sky Sports.
"Although we've won the league tonight we know we've still got two games [left], we want to win those games and be unbeaten all season."
The Blues can still win the treble with an FA Cup final against United to come on May 18 and the Women's League Cup trophy already in the bag.
With AAP.
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