But left winger Sue Smith equalised five minutes later and midfielder Jess Clarke hit what proved to be the winner a minute into the second half.
A third win in four matches lifted Leeds four places in the table and, with games in hand on both Bristol and third-placed Blackburn, they could be set for a top three finish.
Chelsea were expected by many to become a top three club this season, but they will now probably have to settle for mid-table.