The Red Devils ensured the race will go to the final day next weekend by beating Manchester City 2-1 with a stoppage-time goal from Lucia Garcia, leaving Chelsea two points clear of United on 55 points with one round of games remaining.
The Blues also have the edge over United in goal difference and their fate will be in their own hands when they visit relegation-threatened Reading in their last game next Saturday.
Earlier on Sunday, Chelsea eased past Arsenal, with Guro Reiten putting them ahead after sliding in at the far post to turn in an Eve Perisset cross in the 22nd minute.
Captain Magdalena Eriksson, who will leave the London club at the end of the season, followed that up by stabbing in a second from close range following a free-kick to pile the pressure on United in the late kick-off.
United started well and took the lead through Hayley Ladd, and when City had goalkeeper Ellie Roebuck sent off before the break for a foul on Nikita Parris, the United faithful were sure the title chase would live on until the final day.
Instead, they had to endure some anxious moments as United keeper Mary Earps was caught out by a deep cross from Filippa Angeldahl which flew into the net, and it took a late close-range strike from Garcia to give them the points.
Fourth-placed City's defeat means Arsenal are all but certain to finish third as they have a three-point lead and a far superior goal difference.
Bottom side Reading suffered a big blow on Saturday as they lost 4-1 at Tottenham Hotspur and they now face Chelsea next weekend needing a win to have any chance of staying up.
Reading are 12th on 11 points, two behind Leicester City who lost 2-1 at home to West Ham United on Sunday, while mid-table Everton beat 10th-placed Brighton & Hove Albion 2-1 thanks to a stoppage-time goal from Sweden international Hannah Bennison.
The highest-scoring match of the day saw WSL top scorer Rachel Daly net again to take her total to 21 as her Aston Villa side came back to draw 3-3 with visitors Liverpool.
Guro Reiten put Chelsea ahead after sliding in at the far post to turn in an Eve Perisset cross in the 22nd minute, before captain Magdalena Eriksson, who will leave the London club at the end of the season, stabbed in a second from close range following a free-kick.
Arsenal tried to play with more attacking intent after the break, with Katie McCabe missing a penalty, but Chelsea held on for a win that prompted wild celebrations from the home supporters at Kingsmeadow.
