Andy Farrell's men were heavy favourites for this series and they laid down a marker in the opening Test with a dominant performance.
They controlled almost every facet, with the scrum the only area of concern, as the visitors set themselves up perfectly for the final two internationals.
The Lions were particularly excellent in the first half, going 10-0 in front through a Finn Russell penalty and Sione Tuipulotu's try, before Max Jorgensen responded for Australia.
That was their only opportunity in the opening period, however, as the tourists held a 17-5 advantage thanks to Tom Curry's score.
Dan Sheehan then crossed the whitewash to effectively seal the win before the hosts gained some consolation via Carlo Tizzano and Tate McDermott tries.
Few gave the Wallabies had much of a chance before the series and the start from the Lions was ominous. Gone had the poor starts which hampered their early games as they opened in hugely impressive fashion.
The tourists were physical and accurate in the opening 20 minutes, with Tommy Freeman signalling their intent by charging through a couple of would-be Aussie tacklers and charging over the gain line.
Farrell's side duly earned an early penalty, which Russell converted, before they started to create chances with ball in hand.
The excellent box-kicking of Jamison Gibson-Park and the work around set-piece and breakdown was giving them chances in the opposition half and the Scottish playmaker was dictating play nicely.
A superb off-load from the pivot sent Dan Sheehan surging into the 22 and, following a few more powerful carries by the forwards, a wonderful pass from Russell gave Tuipulotu an easy run-in.
It could have been even better for the Lions when a sweeping move on the shortside enabled James Lowe to break free from Jorgensen and find Huw Jones.
The centre was taken down by the right wing just short of the line and he was then penalised, after consultation with the TMO, for a double-movement before touching down.
It was an important intervention from the Wallabies youngster and he would have another one soon after as he got the hosts back into the contest.
The Lions have dominated the aerial battle but, rather ironically, Australia's try came via Jorgensen winning the individual duel with Hugo Keenan to score.
That very much came against the run of play but the visitors simply reset and continued to create opportunities. They were initially profligate with accuracy and execution costing Russell and Lowe, but the pressure would soon pay off.
Once again, the forwards had the Wallabies in retreat and it was Curry who got the glory as went over from close range to give Farrell's men a 12-point buffer at the break.
Australia needed a vast improvement at the start of the second period but it did not materialise as more mistakes resulted in another Lions try.
The lineout, which was an issue in the first half, let the hosts down two minutes after the interval as Curry intercept a throw over the top.
He found Russell, who then then Jones clear, before the openside flanker made an impact by straightening the line and giving Sheehan enough time and space to cross the whitewash.
Even at that point, the opening Test appeared over. Although the Wallabies upped their intensity and physicality, and held onto the ball better, leading to some Lions infringements, the tourists were not unduly troubled.
After spending what seemed like an eternity on the opposition line, they finally got their reward through Tizzano's close-range score.
Another try would have made it interesting, but the Lions quickly earned a penalty in front of the posts, which Smith converted, to kill off the game.
Although McDermott did get another score back, the Wallabies had, by and large, been outclassed by the Lions.