Cooper grabbed two tries - the first a length of the field interception, and the second the last-minute clincher - to break the hearts of the Lions in a 20-6 win at Wigan?s JJB Stadium.
For long periods of the second half the Lions had looked capable of recording the victory that would have gone a long way to making amends for last week's defeat at the hands of New Zealand.
Great Britain had trailed by just two points at 8-6 for much of the second half after Sydney prop Adrian Morley brought them back into it, but late scores by full-back Anthony Minichiello and Cooper put the visitors out of reach.
And the classy 26-year-old insisted it was the Kangaroos' water-tight defence in the face of wave after wave of home attack that was responsible for the win at a rain-lashed JJB Stadium.
Cooper said: ?We pride ourselves on our defence, and our greatest asset is probably our defence. We just hung in there and we were lucky enough to come through.
?It was up there with one of the toughest games I've every played. The conditions certainly didn't suit our style of play, but you have to play in them, and it didn't suit them either.?
The St George-Illawarra Dragons ace's two tries, to add to the brace he scored against New Zealand last month, broke the hearts of a Lions outfit who had a lot of field position but could not find the spark to break through.
Cooper's first score showed off his predatory instincts to perfection.
The Lions had looked on the verge of scoring as they attacked the Australian line, but a speculative pass from hooker Keiron Cunningham found Cooper instead of Martin Gleeson - and despite Brian Carney's heroic chase there was only ever going to be one outcome.
Cooper continued: ?It's always good to score tries, so I'm really happy. The first one I just pinned my ears back.
?I sort of had a look on my left, and I could see him (Carney) coming. I knew I couldn't slacken off, I had to keep going.
?I had a pretty good start on him though, and I knew if I kept in top speed I'd be all right.?
The defeat means Great Britain now need good wins against both New Zealand and Australia in their final two group games to have any chance of making the final.
But Cooper was full of praise for the efforts of Brian Noble's men.
He added: ?It was a pretty tough game. Great Britain certainly gave us a good fight out there. They played well, we were just lucky to get the victory.
?They played well. They should be, not happy, but they did play really well. They have got a tough two games coming up, though, and they're going to be hungry for it.
?It's early days but the win will give us a lot of confidence, that's for sure, and we'll go over to France and have a game over there before we play Great Britain the week after that.
?But we're pretty confident we can win the tournament.?
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Thanks to www.superleague.co.uk for this article.Like