Duggan cancelled out fellow England ace Eni Aluko’s opener as league leaders Chelsea dropped points for only the second time this season.
Watch the highlights of the game at the Academy Stadium
Aluko broke the deadlock on 23 minutes though, dissecting the defence with a flicked pass to Ji So-Yun and making no mistake from close range when the South Korean returned an inch-perfect square ball before Duggan levelled on 37 minutes.
There was disappointment for Arsenal on Saturday after Nikki Watts stole a point for Bristol Academy who have drawn their last two matches after losing their first four in the FA Women’s Super League with BT Sport.
Chioma Ubogagu had swept Arsenal into a first-half lead but Watts was on hand to level things just after the break.
Elsewhere Fern Whelan’s second-half header was enough to secure Notts County’s third successive league victory as they edged a tight clash with Liverpool.
And a first-half blitz gave newly-promoted Sunderland an emphatic 3-0 victory over Birmingham.
Beth Mead gave Sunderland the lead after 25 minutes before Brooke Chaplen added a second from close range and Vicky Greenwell rounded off proceedings with a sublime free-kick on the stroke of half time.
Watch highlights of Sunday's WSL 1 game
