The 24-year-old American was the star in a dominant display at McKellar Park which took Canberra to 27 points and just three behind leaders Melbourne City.
In the other ALW clash, Perth Glory came from behind to beat Newcastle Jets 3-2 away, courtesy of a Tijan McKenna strike in the 86th minute.
The win took the Glory into fifth position and put the ninth-placed Jets' finals hopes on the rocks.
Canberra captain Michelle Heyman also found the net against the Wanderers in 35-degree heat, which forced the players to have two drinks breaks in each half.
A challenging cross from Bethany Gordon wasn't dealt with by the Wanderers defence and it fell for Aulicino to slot it home with her left foot with precision in the 11th minute.
Aulicino hit the crossbar moments later and Gordon and Aulicino again then drew stunning saves from Shamiran Khamis as the hosts threatened.
Wanderers forward Amy Barker had a challenging shot from long range parried away by Canberra goalkeeper Sally James in the early minutes.
It didn't take long for Canberra's veteran striker Heyman to assert herself and it took three defenders to stop one raid.
Heyman, called into Australia's squad for the upcoming Asian Cup, oozed confidence early.
She hit the post and the side netting late in the first half as she went in search of breaking an eight-game streak without scoring coming into the match.
The hosts had 14 shots on goal in the first half and would have been well ahead had it not been for the brilliance of Khamis who showcased once again why she is one of the best goalkeepers in the ALM.
Aulicino crunched a right-footer home in the 66th minute and nine minutes later Heyman ended her goal drought with a close-range effort after a curling corner eluded Khamis.
In Newcastle, the Jets scored the opener in the 16th minute through Emma Dundas after Sophie Hoban dispossessed McKenna and hit the post with her shot. Dundas swooped on the rebound with panache.
Striker Gabby Hollar got one back for Glory on the cusp of halftime when she chipped the goalkeeper with a goal of pure class.
The Jets regained the lead in the 61st minute with a classic volley from striker Melina Ayres after a Lauren Allen cross.
Glory's Clancy Westaway scored her first ALW goal eight minutes later to set up a thrilling final 20 minutes.
It was McKenna who stole the match late for Perth when she walloped home a deep corner by Isobel Dalton.
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