A maiden cirst class half-century from Calum MacLeod gave Scotland some respite on a day dominated by Australia's second string at The Grange, Edinburgh.
The visitors first increased their overnight total to 372-8 before reducing the Scottish innings to tatters at 44-6.
MacLeod's battling counter-attack, aided by cameos from Matthew Cross and Iain Wardlaw, helped hoist the total to a more respectable 149 but the Australians had taken their lead to 388 runs by the close.
Skipper Preston Mommsen last night admitted a draw is the best his side can hope for. "Our batting didn't go to plan and our shot selection let us down which was disappointing," he said.
"Having said that, Australia bowled really well and put the ball in good areas and with good pace. They have the ability to move the ball both ways – in the air and off the seam – and you could see they have played at a higher level.
"But Calum and Iain showed that it is possible to score runs against them and if we had been able to put a partnership together earlier on we could have put a decent total on.
"The best we can hope for realistically is to draw. It will be tough because Australia are calling the shots but we know we will be batting again at some point and we have to stick to our plans and learn the lessons of today."
They never fully recovered from a disastrous start during which the top order looked mesmerised by a high-class bowling attack.
Josh Davey was given a torrid working over by the pacy James Pattinson who sent down two consecutive maidens to the Middlesex man before having him caught by Alex Doolan.
Opening partner Matt Machan enjoyed an easier time against the raw Chadd Sayers, whom he drove through the covers for four twice in one over.
Machan was then involved in a mix-up that cost Freddie Coleman his wicket and may still have been contemplating his part in his team-mate's downfall when, having made 21, he took a reckless charge at Lyon's second delivery to be comfortably stumped by Brad Haddin.
Scotland were in danger of total collapse when Richie Berrington was bowled by a brute of a delivery from Pattinson.
Mommsen and Moneeb Iqbal survived until lunch but not much longer, the latter going for a 20-ball duck. The skipper went in the next over, edging Peter Siddle behind to depart for 12.
Scotland finally conjured something approaching a partnership when Cross and MacLeod came together with the score on 44-6.
However, having reached 17 in a stand of 34, debutant Cross waved his bat at a wide delivery from Moises Henriques and gave the simplest of catches to Haddin.It was a sad end to a promising knock and sparked another collapse which saw Gordon Goudie and Calvin Burnett both fall for ducks to the teenage left-arm spinner Agar.
That left to Wardlaw to join MacLeod in the highest stand of the innings as a flurry of boundaries took both players to their highest first-class scores.
But the latter was caught in the deep by Agar to leave Wardlaw unbeaten on 33, and Scotland on a meagre total of 149.
A few eyebrows were raised when Haddin declined to enforce the follow-on. And, as in the first innings, the Australian top order was less than convincing.
Youngster Jordan Silk edged MacLeod to Machan at slip for 22 while Machan took a second catch to remove Ashes prospect Usman Khawaja off Goudie.
Doolan, though, survived for longer, hitting seven boundaries on his way to 47.
However, his innings was cut short when Burnett trapped him in front to claim a maiden first-class wicket, while Iqbal removed Steve Smith before the Aussies closed on 165-4.
Earlier Siddle had duly completed his maiden first-class century, demonstrating his graduation to genuine all-rounder status with a knock of 103.
There was a wicket each for Scotland's main strike bowlers, Wardlaw and Goudie, before Aussie skipper Haddin signalled the declaration.
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