On the back of five clean sheets in their previous seven matches, an uncharacteristic Scottish defensive error from Alan Hutton gifted Poland the lead just after the ten-minute mark, with Kryzsztof Maczynski finishing well from just outside the box.
The visitors were far from overawed however, and were quickly level after Shaun Maloney’s third goal for Scotland finished off a fine move.
Scotland then completed the turnaround, with Steven Naismith getting the slightest of touches to a free-kick which was floated in by James Morrison to send the visiting Tartan Army into raptures.
The Scots were looking comfortable, but their resistance did eventually give when Arkadiusz Milik fired an equaliser past Marshall to ensure a nail-biting final 14 minutes.
And Poland should have infact snatched all three points, with Kamil Grosicki denied by the post with the goal at his mercy.
The result sees Scotland remain third in the group, with hopes of qualification for their first international tournament since 1998 still in the balance. Poland stay top.
The Poles still clearly buoyed by their weekend victory over World Champions Germany started rather sluggishly, but the hosts were really gifted an early lead by Aston Villa full-back Hutton.
Under little pressure, Hutton chose to take a touch before clearing on the edge of his penalty area, but he miscontrolled, inadvertently laying the ball into the path of the onrushing Kryzsztof Maczynski, who stroked the loose ball into the bottom corner, leaving Marshall no chance.
However, Scotland are in excellent form themselves, and were not be deterred, with a real team goal levelling proceedings just seven minutes later.
Steven Fletcher’s pinpoint diagonal lofted pass picked out Ikechi Anya, who controlled brilliantly, and laid the ball back to Maloney, who side-footed past Arsenal goalkeeper Woijech Szczesny in the Poland goal to equalise.
Five minutes before the break, Steven Whittaker saved Hutton’s blushes again, as he looked for an offside decision which wasn’t forthcoming, with the Norwich defender having to come across to clear with Marshall stranded.
After the interval Milik almost got the home side back in front, prodding a knock-down goalwards, but it flew just over the top, with Marshall beaten.
With Poland looking very dangerous down the other end, a timely strike by Naismith put the visitors in front for the first time in the match.
Morrison’s long-range free-kick looked to be too far out to cause any real danger, but the West Brom midfielder managed to pick out Naismith at the back post, and the Everton forward delightfully flicked his fourth Scotland goal past the despairing dive of Szczesny.
Milik then had a great chance to equalise after Scott Brown diverted a cross into his path, but the 20-year-old headed over from point-blank range.
The relatively quiet Robert Lewnadowski almost got a toe to a low cross as the home side pushed for an equaliser, but Scotland were looking relatively comfortable.
Maloney forced a fine save out of Szczesny after more great work from Anya down the left flank as Scotland looked to wrap up a vital victory.
However, Milik finally did get his goal to break Scottish hearts on 78 minutes.
A wonderful lay-off from Artur Jedrzejczyk put Milik in behind Hutton, and he made no mistake, rifling the ball past Marshall to raise the roof of the Warsaw National Stadium.
It was all Poland after the equaliser, Lewnadowski coming close to finding a winner, cutting inside and unleashing a ferocious effort at goal, only to be denied by a fantastic save from Marshall to his left.
Then, as Grosicki rounded Marshall the Poles looked set to snatch all three points, but the Stade Rennais midfielder hit the post from a matter of three yards to ensure it was honours even in Warsaw.