In a pulsating game that had four goals, two penalties, a red card and eight yellows, the crisis-stricken Reds twice led but relinquished the advantage on both occasions as their winless run was extended to six matches.
But it was a much-improved performance from Adelaide, who produced their most passionate and committed display in some time in what has been a tumultuous week for the club with the sacking of coach Rini Coolen.
New boss Kosmina, in his first game in charge of an A-League club since he was dismissed by Sydney two and a half years ago, was booed loudly by the home fans whenever he appeared on big screen but will have been content to take a point away from the match.
The Reds twice took the lead with goals from Daniel Mullen and Dario Vidosic, but were pegged back on both occasions with Karol Kisel (penalty) and Dimitri Petratos scoring for the home side.
Adelaide midfielder Iain Ramsay had the best chance of the final stages to win the match, but his shot was well saved by Sydney goalkeeper Liam Reddy.
Ramsay's disappointment was compounded close to the end was he was sent off for a second bookable offence.