In an entertaining encounter at Allianz Stadium on Saturday night, Sky Blues striker Apostolos Stamatelopoulos opened the scoring in the 50th minute with a close-range header.
It was level pegging eight minutes later when Eli Adams slammed one home for the Jets, but Arslan thought he had won a penalty in the 87th minute when he was barged over by Daniel Wilmering in the box.
There was doubt about whether Wilmering was shoulder-to-shoulder or slightly behind Arslan.
Arslan threw his arms up in despair after the referee waved play on, with the moment proving to be the last flashpoint of the pulsating match.
The second leg will be played in Newcastle, where the Jets will be aiming to snare a win in front of their home fans at McDonald Jones Stadium next Saturday night.
"The performance was great. That's been our best performance since I've been here," said Sydney FC coach Patrick Kisnorbo, who arrived in late March following the exit of Ufuk Talay.
"We scored a pretty good goal. A lapse of concentration (led to their) equaliser.
"But overall I can't fault the players, because they gave everything tonight."
Jets goalkeeper James Delianov had a busy night, with the Sky Blues unleashing 15 shots, including six on target.
"I'm not over the moon with the result, but we'll take it," Jets coach Mark Milligan said.
"The title was never going to be decided tonight. It's a tough place to come.
"We had to adjust a few things at halftime in terms of our press, and in the second half I thought we were more than comfortable."
Newcastle, who are aiming for the treble this season after winning the Australia Cup and finishing top of the ladder, were making their first finals appearance since losing the 2017/18 decider.
Sydney, already with five titles to their name, entered the match on the back of their 1-0 elimination final win over Melbourne Victory.
Only five Jets players had tasted A-League finals action before - and none while playing for Newcastle.
There were no goals in the first half but plenty of edge-of-your-seat moments as both sides embraced attacking football.
Sydney defender Rhyan Grant hit the post with a fourth-minute header, and Piero Quispe unleashed a curling strike in the 28th that forced a fine diving save from Delianov.
Newcastle's best chance of the half arrived in the 33rd minute, when Adams had his header blocked on the line, before the hosts held their nerve in a goal-line scramble just as Mark Natta looked set to poke the ball home.
A clever bit of body work from Stamatelopoulos after a teammate's shot had been deflected high into the air proved key to the opening goal.
After edging Natta out of the drop zone, Stamatelopoulos was able to head the ball past the advancing keeper for what was just his third goal this season.
The lead was short-lived, with a 60m fast break from Clayton Taylor setting up Adams for the equaliser.
