Western United unleashed 22 shots to six in Sunday's match at Coopers Stadium, but it was Adelaide defender Matilda McNamara's header from a corner in the 24th minute that proved the difference.
It marked Adelaide's first win in a final in their 17-year ALW history, and they will now take on second-placed Melbourne Victory in a two-legged semi-final.
"It feels pretty unreal. I'm a bit in shock," Adelaide goalkeeper Claudia Jenkins told Paramount.
"In the second half, we were expecting them to come out pretty aggressive.
"We did really well to withstand that. We withstood the wave and are still standing.
"The message was received, we dug deep, fought to the end and got the result."
Central Coast's home elimination final against Canberra United had to be postponed until Monday evening after torrential rain left the pitch in Gosford waterlogged.
The fourth-placed Mariners were due to host Canberra at Industree Group Stadium on Sunday afternoon.
But the pitch was deemed unplayable, forcing the game's postponement until Monday evening - provided the playing surface is up to scratch by then.
"Following extensive rain in Gosford in the last 24 hours, and up to 50mm of rain still to fall today, the water-logged pitch has been deemed unplayable," the Australian Professional Leagues said in a statement.
Adelaide looked lively in the first half of Sunday's do-or-die match, with Emily Condon's early strike well saved, before McNamara gave the hosts the lead.
It could have been 2-0, but Lucia Leon's 34th-minute shot from just inside the box hit the post.
At the other end, star United striker Chloe Berryhill (nee Logarzo) also struck the woodwork just before half-time.
United pushed hard for an equaliser in the second half but couldn't find a way through.
It is the second season in a row that Western United bombed out in an elimination final.
"It was just one of those days pretty much," United midfielder Catherine Zimmerman said.
"I'm pretty proud of how we played. We battled and we created a lot of chances, we just couldn't score."
The winner of the Central Coast versus Canberra elimination final will take on premiers Melbourne City in a two-legged semi-final.
11°C