A bumper crowd of 17,198 rocked up to get a glimpse of Sturridge on Saturday night, but it was Bruno Fornaroli who sent them wild in the first half with his 30-yard thunderbolt that levelled the scores.
Adelaide striker Kusini Yengi had given the visitors the lead in the 22nd minute.
Sturridge, who only trained with the team for the first time on Monday, entered the fray in the 85th minute, and he touched the ball just twice during the nine minutes he was on the field. His first touch was a neat knee-foot combo to pass to a teammate, while his second touch was a deflected cross.
There were four minutes of added time in the match, but Sturridge was starved of opportunities and couldn't pull off a stoppage-time winner.
"I'm not going to take too much from that," Glory coach Richard Garcia said after the match when asked about Sturridge. "What we've seen in training has been good, and it's about him now building up and finding his feet and getting fitness - he needs to play games."
Former Liverpool goalkeeper Brad Jones made a nervy start to Saturday's match, with his attempt to be too cute after receiving a pass from a Glory teammate almost costing his side a goal.
Jones waited too long before deciding to get rid of the ball. His rushed pass deflected to Yengi, whose shot from close range sailed wide.
Glory received another reprieve just minutes later when Ryan Kitto's shot struck the post and bounced away. But Adelaide finally had their reward in the 22nd minute - albeit in somewhat controversial circumstances.
Adelaide midfielder Ben Halloran used his pace to skip pass a Glory defender before squaring the ball to Yengi, who stuck out his left foot to deflect the ball in.
Glory players were left furious after believing Halloran had bowled over a Perth player in the lead-up, but their pleas fell on deaf ears.
Perth struggled to create clear-cut opportunities in the first half, so Fornaroli created one out of nothing when he unleashed a mesmerising strike from 30 yards out.
The ball struck the inside of the post and went in, sending the crowd wild.
Adelaide put the ball into the back of the net early in the second half but the whistle had already sounded for a foul on Glory defender Jack Clisby.
"I was a little bit unsure why our second one was ruled out at the other end," Adelaide coach Carl Veart said. "I'd like to see the replay for that. I don't know what the free kick was for. It looked like a good goal."
Glory suffered their own disappointment when they had a 55th-minute goal from Antonee Burke-Gilroy ruled out by the VAR, with replays showing Fornaroli was just marginally offside in the lead-up.
Perth will be sweating on the fitness of Andy Keogh after the veteran striker limped out early in the second half with a calf injury.