The veteran, Australia's all-time leading scorer, is now 36 and playing for A-League club Melbourne City after ending a brief spell in the lucrative Chinese Super League.
But the former Millwall, Everton and New York Red Bulls favourite has retained his uncanny knack for delivering when it counts on international duty, meeting Brad Smith's cross to slot home from close range with 15 minutes to go at Mohammed Bin Zayed Stadium in Abu Dhabi.
The victory, secured by Cahill's 48th goal in 92 appearances, sees Ange Postecoglou's team retain a 100 per cent record from two matches played in the third round of Asian Football Confederation qualifying for the 2018 World Cup in Russia.
Asian Cup holders Australia, who defeated UAE 2-0 in the semi-finals of the regional competition en route to glory on home soil in January 2015, created the first real opening of the game after 16 minutes.
Tomi Juric found Robbie Kruse inside the area, the forward shooting across goal and seeing his attempt well saved by Khalid Essa.
A tense opening period produced few genuine chances, although Rogic, teed up by a Juric lay-off, saw a deflected shot parried over the bar by Essa in first-half stoppage time.
The visitors were perhaps fortunate to retain a full complement of players when Rogic was only booked for a stamp on Omar Abdulrahman four minutes into the second period.
