Canberra appeared set to escape from Saturday's physical encounter at McKellar Park with their first clean sheet of the season - and a win to hoist themselves off the bottom of the ladder.
But that was before American striker Morris, brought on from the bench, seized a pass from Sophie Harding and broke up field to set up a one-on-one with Coco Majstorovic.
Morris's shot sailed past the Canberra goalkeeper to lock up a draw in the seventh and final minute of stoppage time.
The result enhances the Wanderers' finals push, moving them level on points with sixth-placed Newcastle who face Melbourne City on Sunday.
Struggling Canberra had taken an unlikely lead just before the hour mark.
Fresh from starring in the Matildas' demolition of Uzbekistan late last month, Michelle Heyman sent a glancing header to Nickoletta Flannery, who slipped the ball into the net at close range.
Canberra will have the chance to exact revenge for Morris's 11th-hour goal when they travel to Wanderers Football Park for a rematch on Wednesday.
Their defender Holly Murray appears in doubt for the clash after being substituted with a left-leg injury in the second half.
Central Coast goalscorer Kyah Simon (r) challenges for possession with Brisbane's Ayesha Norrie. (Darren England/AAP PHOTOS)
The Central Coast Mariners kept their premiership dream alive with a 2-0 defeat of Brisbane Roar that featured two goals in a minute either side of halftime.
The Roar enjoyed the better of the chances in the first half at Ballymore Stadium, but Wurigumula drew first blood for the Mariners in the 45th minute.
Annabel Martin looped a long cross into the box for the China international, who poked the ball into the bottom-right corner of the net.
Brisbane did themselves no favours after the break.
Seconds after the resumption, Alicia Woods mistimed an attempted pass to Leah Scarpelli as the Roar looked to defuse a Mariners corner.
Martin pounced on the loose ball and fired it to Matildas forward Kyah Simon for the visitors' second goal.
The win moved the Mariners up to second.
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