Spaniard Diego Castro put Perth in front in the 16th minute before Joel Chianese claimed a second on the half hour mark as Kenny Lowe's team defeated City just a week after seeing his side win a nine-goal thriller between the teams in the regular season.
Perth will now take on regular season table-toppers Sydney FC on Saturday with a place in the Grand Final against either Melbourne Victory or Brisbane Roar at stake.
"The biggest thing was they changed their shape to counter us," Lowe told Fox Sports. "I thought it was surprising, it gave everyone in the change room a massive lift.
"We came out full of confidence from the games we've played them. But to see they changed their shape to suit us was quite amazing."
Brisbane Roar will take on Melbourne Victory in the other semi-final next Sunday after John Aloisi's side beat former Asian champions Western Sydney Wanderers in a penalty shootout on Friday.
Terry Antonis' penalty gave Western Sydney the lead before an equaliser from Jamie MacLaren took the game into extra-time and then a shootout, where Brisbane emerged 6-5 winners thanks to the performance of substitute goalkeeper Jamie Young.
"You have to have a bit of luck to win a penalty shootout but the luck went our way because we were very good after that first half," said Brisbane coach John Aloisi.
"A lot of teams when they play so badly in the first half won't be able to recover. We were 1-0 down but the fans helped the players, the players started believing and some of the football we played in the second half and extra time was brilliant."
(Reporting by Michael Church in Hong Kong, Editing by Pritha Sarkar)
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