The Republic have been revived since Trappatoni took charge 15 months ago, but the Italian would have been unhappy with his side's display - only his second defeat in charge - less than a month before their key World Cup qualifier in Cyprus on September 5.
The hosts lacked the required cutting edge to break down a side who have already booked their tickets to the finals in South Africa, and were given a lesson in finishing by midfielder Cahill whose clinical touch after 38 and 44 minutes virtually settled the game.
An impressive Australian performance was given further gloss in stoppage time when David Carney thrashed in an unstoppable 30-yard drive.
Trapattoni made one change to the starting line-up he prematurely named on Tuesday night, bringing in Darron Gibson for Keith Andrews.
Australia midfielder Marco Bresciano started to win his 50th cap while their clubless skipper Lucas Neill was not named in the squad, to inspire speculation he had flown out to complete a move to an unnamed club.
In his absence Fulham goalkeeper Mark Schwarzer took the captain's armband.
Australia started the brighter with Luke Wilkshire firing wide from the edge of the area before Harry Kewell forced Shay Given into a low save from a rehearsed free-kick.
The Republic were playing a home game outside Dublin for the first time since 1985, and a first in Limerick, but they were slow to find their feet in the new surrounds of Thomond Park.
Eventually they found some continuity, most notably down Aiden McGeady's left flank, with the Celtic winger crossing for Robbie Keane who spooned a header over from six yards.
Damien Duff then saw a goalbound effort blocked by Carney following a breakaway before Keane was then expertly denied by Schwarzer from close range after McGeady had played him in after a mazy run.
The Republic were in control and might have been rewarded on the break if Gibson had spotted Keane's run down the middle, instead over-hitting a pass for Doyle that slid out.
The home side's profligacy proved costly as Australia hit them on the counter-attack after 38 minutes.
Scott McDonald and Cahill were Australia's only attackers as they forged forward, but they combined superbly to free the Everton man who slid a low show past a static Given from the edge of the area.
The visitors cold have had another moments later when Kewell got behind his marker only to head over from six yards.
A second did arrive, however, a minute from the break and it was Cahill again.
Rhys Williams was allowed a free run into the area before unleashing a fierce shot that Given could only block as far as Cahill to poke home and register back-to-back two-goal game for his country.
With his work done Cahill was substituted at the break, while Trapattoni brought on Stephen Hunt and Caleb Folan for Duff and Doyle respectively.
The Republic still looked shocked from Cahill's two-goal salvo and were lucky his replacement, Brett Holman, shot straight at Given after he was afforded time to pick his spot from the edge of the area.
Hunt, who is expected to be unveiled as a Hull player on Thursday, provided some much needed energy but like his team-mates he, too, lacked a telling final touch.
He first over-hit a free-kick to allow Schwarzer to easily gather before shooting wide after a clever Keane backheel.
Keane then turned his marker in the area but his goalbound shot was blocked by a Carney.
The hosts continued to waste chances with substitute Keith Andrews hitting a post, before Sean St Ledger headed straight at Schwarzer from six yards.
And again they were made to pay by Carney's superb stoppage-time strike, and give Trapattoni plenty to think about ahead of the Mediterranean trip next month.