\ at Hampden Park.
There was little between the sides until Tierney scored his first international goal to make it 1-0.
Scotland looked to be heading for victory until Piatek scored from the penalty spot in stoppage time.
Steve Clarke’s side will play Austria away next week in the second match of their friendly double header, with Wales waiting in the play-off final in Cardiff should the Scots eventually get past Ukraine.
In the absence of Covid-affected captain Andy Robertson, midfielder McGinn was handed the armband as he came up against Aston Villa team-mate Matty Cash.
Nathan Patterson was installed at right-back despite his struggle to make an impact at Everton since joining from Rangers in January but a strong Scotland side included Scott McTominay, Grant Hanley and Tierney in a back three with Che Adams leading the line.
First-time call-ups Ross Stewart, Craig Halkett and Aaron Hickey were on the bench as was Poland’s star striker Robert Lewandowski as new boss Czeslaw Michniewicz kept an eye on their World Cup play-off against either Sweden or Czech Republic next Tuesday,
There was a huge Polish support among a healthy Hampden crowd of 39,090 for a game where £10 from each ticket was going to support UNICEF’s efforts in Ukraine.
The vociferous away fans added to the atmosphere but it was the Tartan Army who were cheering Patterson in the 10th minute when he skipped past four Poland players on a lengthy run before his left-footed shot from 16 yards was saved by keeper Lukasz Skorupski.
In the 23rd minute Poland wasted a glorious chance to take the lead when defender Bartosz Salamon headed a cross from Cash over the bar from inside the six-yard box.
The Scots finished the half strongly.
In the 34th minute Adams tried his luck from 25 yards with a powerful drive which Skorupski did well to gather.
Just before the break Patterson had two efforts saved by Skorupski, the second of which came in the same incident which saw the Polish keeper also deny midfielder Billy Gilmour, before Ryan Christie headed wide moments later.
First-half substitute Piatek sent a drive wide of Gordon’s right-hand post early in the second half after the Scotland defence had been split open – but the home side responded positively.
McGinn went round Skorupski after being sent through by Gilmour but his touch was too heavy and he ran the ball out.
In the 65th minute, after McTominay lost possession in the centre of the pitch to Sebastian Szymanski, the Pole drove forward and Piatek’s drive was cleared off the line by Gilmour
Hickey then replaced Greg Taylor to make his debut, with Stephen O’Donnell on for Patterson. Moments later the Scots were ahead.
McGinn’s whipped-in free-kick from wide on the right was met by the Arsenal defender, who glanced a header past Skorupski for his first Scotland counter in 31 caps.
Stuart Armstrong, Kenny McLean and Ryan Jack replaced Christie, Callum McGregor and Gilmour but jus as the game looked like ending in a morale-boosting win, the penalty was conceded and the home side had to settle for a draw.