Williams scored the winner for Everton, who were far from convincing
Everton moved to the top of the Women's Premier League with a 2-1 local derby win at Liverpool, England midfielder Fara Williams netting the winner.
Birmingham City lost 4-2 at Bristol Academy, with Gwennan Harries scoring twice for the home side.
Nottingham Forest have now lost all three of their matches.
Newly promoted Forest trailed 3-0 at the break and went on to lose 4-1 against Doncaster Belles, who hit four for the second successive game.
Liverpool 1-2 Everton
Everton were well below par but came from behind to grab victory.
Liverpool, hammered 11-2 by Arsenal on Sunday, took the lead through a 32nd-minute penalty by Cheryl Foster.
Full-back Becky Easton, the one Everton player to shine, equalised in the 59th minute.
And Williams, who hit a hat-trick in Sunday's 4-1 win at Fulham, headed in the winner 16 minutes from time.
The Toffees top the table with a 100% record, but they could be overtaken on goal difference by either Arsenal or Chelsea after Thursday evening's matches.
Bristol Academy 4-2 Birmingham City
Harries, Stef Curtis and Justine Lorton hit first-half goals to put Bristol well on the way to a comfortable victory that Harries wrapped up with her second strike just before the hour.
Birmingham had far more of the possession in the second half but their goals, scored by Maz Gauntlett and Natasha Lynch, did not arrive until the last three minutes.
Nottingham Forest 1-4 Doncaster Rovers Belles
Donny hit four goals for the second time in two games to leave newly promoted Forest without a single point to date.
The game was as good as won by half-time, when Donny led 3-0 through goals by Liz Hansen, Rachel Williams and Suzanne Davies.
A 75th minute own goal by Kelly Finley sealed Forest's fate, though Andi Bell grabbed a consolation effort a minute from time.
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