Andersson, on the left of Chelsea's midfield, played Bethany England to the lead in the 19th minute.
A result Chelsea saw to be able to bring into the locker room, but in the penultimate minute of the first half, Kerry's Harrop equalized.
Chelsea's answer?
2-1 two minutes later.
Samantha Kerr's header in extra time also stood over the goalless second half.
It was Kerr's 18 goals for the season and she tops the shooting league.
Swedish trio Andersson, goalkeeper Zecira Musovic and midfielder Magdalena Eriksson played the entire match.
With two games left, Chelsea tops the league, four points ahead of Arsenal, who, however, have three games left.
Jonna Andersson made it clear a few weeks ago that she will leave Chelsea after the season and continue her career in Hammarby in the damallsvenskan.