Willie Kirk's second-place side have seven points from three games, level with leaders Manchester City, who thrashed Bristol City 5-0, and also with title holders Chelsea who beat West Ham United 2-0 on Saturday.
Captain Aileen Whelan struck at the far post from a freekick in the 60th minute to give Leicester a surprise lead, having frustrated their hosts for an hour.
However, defender Maya Le Tissier equalised seven minutes later when she headed home Katie Zelem's corner to the delight of the home fans.
Leicester have been a revelation early this campaign, unbeaten in their first three games after a 10th-place finish last season.
The 30-year-old said in an Instagram post that the jersey sold out on Monday, the same day it was released.
Persons:
Manchester United's Alessia Russo, Jason Cairnduff, Willie Kirk's, Captain Aileen Whelan, Maya Le Tissier, Katie Zelem's, Kirk, Hinata Miyazawa, Malard, cradling, United, Gabby George, Marc Skinner, Gabby, Mary Earps, Earps, Lori Ewing, Christian Radnedge
Organizations:
Soccer, League, Manchester United, Leicester City, Leigh Sports Village, Rights, Super League, Manchester City, Bristol City, Chelsea, West Ham United, United, Leicester, Nike, Thomson
Locations:
Leigh, Britain, Manchester, Rights MANCHESTER, England