England gave themselves a great chance of an historic series victory over Australia after recovering from an ominous start to crush the Wallabies 39-28 at Suncorp Stadium.
Early tries by Michael Hooper and Israel Folau threatened to overrun the Grand Slam champions but they responded magnificently with Jonathan Joseph, Marland Yarde and Jack Nowell crossing.
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The boot of Owen Farrell, who had replaced George Ford at fly-half, did the majority of the scoreboard damage as England sealed only their fourth victory Down Under in 18 matches.
Nowell plundered his try in the final minute of a pulsating showdown in Brisbane as Australia went in search of a match-winning try of their own.
England head to Melbourne for next Saturday's second Test knowing one more win would complete a series triumph over the World Cup finalists and identify them as a genuine force in the global game.
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Head coach Eddie Jones remains unbeaten since taking over at Twickenham and now has seven Test victories in the bank, but the most recent of these - against the side he once coached - is by far the most precious.
James Haskell had clearly listened to Jones' demand for England to play 'bodyline' rugby as he smashed David Pocock backwards with a thunderous tackle, but it was Australia who made the stronger start and they crossed inside the opening 10 minutes.
The warning signs were there as only a turnover on the whitewash by Maro Itoje prevented a Wallabies try, but they were more accurate shortly after when a fine break by Folau created the space for Hooper to score.
Jones had predicted Australia would come out "breathing fire" and he was proved correct as they tore into the breakdown and repeatedly broke the gain line, creating space almost at will.
The Wallabies were irrepressible as they renewed their assault once more and this time it was Folau who touched down, skipping around a tackle from Farrell after England's defence had been stretched to breaking point.
A Farrell penalty got England off the mark but it was still one-way traffic as they struggled to cope with Australia's pace and power - at least until a dose of good fortune fell their way.
Two missed touch-finders resulted in the Wallabies being pinned back in their own 22 and the deficit was slashed further when they were penalised at the breakdown with Farrell punishing the error.
Bernard Foley appeared to have added a stunning solo try but obstruction by Rory Arnold on Luther Burrell that created the initial opening resulted in it being ruled out.
Farrell ran hard and straight and made ground and once Australia had been penalised once again - they now trailed 8-1 on the penalty count - the Saracens fly-half was on target with the three points.
And just as the half-hour mark passed, England seized the lead when two hare-brained passes were pounced on by Joseph who hacked ahead, gathered and touched down.
Honours were even at the scrum with each side winning penalties which were kicked by Farrell and Foley respectively, with the British and Irish Lion having the final say of the half.
England made the best possible start to the second period when a line-out drive ended with Haskell peeling off the back and striding 20 metres before being halted.
The respite for Australia was only temporary, however, as two phases later Ford - who had replaced the injured Burrell - used a brilliant long pass to give Yarde a simple run in.
Farrell continued to hit the mark from the kicking tee as England stormed 29-13 ahead, but the Wallabies hinted at their own fightback when Hooper produced a fine finish after good work from Folau.
Farrell appeared to have given England some breathing space with his sixth penalty, but when Tevita Kuridrani powered over, the lead was reduced to 32-25 after Foley converted.
A nail-biting climax awaited and the nerves only intensified when Foley kicked a long-range penalty with two minutes remaining to offer sight of victory.
Instead, it was England who had the final say when Nowell collected Ford's superb kick and touched down to start the victory celebrations.