Chapman scored Arsenal's second with a long-range free-kick
Leaders Arsenal and second-placed Everton both collected victories as the Women's Premier League title chase built towards a thrilling finale.
Arsenal beat Bristol 3-0 while Everton, eight points behind but with three games in hand, won 1-0 at Watford.
Nottingham Forest climbed out of the drop zone with a 1-0 win over Leeds.
That meant Liverpool, held in their final match to a 2-2 draw by basement team Fulham, will be relegated along with the Cottagers.
Chelsea look set to clinch third spot finish after a 1-0 win at Doncaster Belles lifted them six points clear of Birmingham, who drew 1-1 with Blackburn.
Arsenal 3-0 Bristol Academy
Arsenal's last home match of the season ended in a comfortable-looking scoreline, but they needed two penalties to assure themselves of victory.
A Kim Little spot-kick gave them a 10th-minute lead that Katie Chapman doubled from a long range free-kick in first-half stoppage time.
Academy battled throughout the second half to force their way back into the game, but the result was settled with a Suzanne Grant penalty five minutes from time.
Watford 0-1 Everton
Everton had the better of the game but Watford wasted a couple of good goalscoring opportunities before Fern Whelan headed the winner just after the hour.
Doncaster Rovers Belles 0-1 Chelsea
An Emma Whitter goal in first-half stoppage time was enough to give Chelsea a rapid double just seven days after beating the Belles at home.
Birmingham City 1-1 Blackburn Rovers
Birmingham moved four points clear of fifth-placed Doncaster thanks to a Karen Burke own goal after Rhiannon Roberts had put Blackburn in front.
Nottingham Forest 1-0 Leeds Carnegie
Andi Bell struck seven minutes from time set up the celebrations for Forest, promoted 12 months ago and assured through this victory of a second season in the top flight.
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