With eight minutes left the 21-year-old Hannover striker came off the bench to nod home a fine cross by Sivasspor winger Kamil Grosicki in an otherwise tepid match played in a near-empty Woertherseestadion stadium.
Poland fielded an experimental line-up that did not feature the likes of Robert Lewandowski, Wojciech Szczesny, Lukasz Piszczek or Jakub Blaszczykowski as coach Franciszek Smuda tested his fringe players ahead of the finals.
Indeed, the purpose of what was essentially a training match was to cull three of Smuda’s 26-man squad, although for most of the match Poland were so average that he may well have left the lot behind.
The weakened team did boast debutant Rafal Wolski, who spurned the chance to open his international account by firing too close to Pavels Dorosevs on 20 minutes.
The Latvia keeper, a free agent, also denied Rafal Murawski, while experienced Poland defender Marcin Wasilewski - who at one point barked at his team-mates in frustration at a sluggish performance - hit the post with a header late in the first half.
But Arsenal reserve keeper Lukasz Fabianski, standing in for team-mate Szczesny and one bright point for Smuda, was the busier between the sticks as Latvia looked dangerous on the break.
Fabianski, who wants to leave Arsenal after falling behind his compatriot in the pecking order, kept out several crosses and long-range efforts, making a decent stop from Ivans Lukjanovs’s fine strike, while Latvia defender Oskars Klava headed just over from a corner.
It was goalless at half-time and if the opening period was a disappointment, the second was a dirge.
Grosicki was quick and nimble down the left wing but his team-mates showed little interest in matching his runs, with Trabzonspor forward Pawel Brozek - who barely figured in a six-month loan spell at Celtic this season - particularly disappointing.
The closest anyone came to a chance of note in the second half was on 56 minutes when Sebastian Boesnich - a former Germany U21 international defender who has since pledged his allegiance to the land of his birth - headed into the side netting after a free-kick from wide.
The match degenerated into a scrap, with several players booked and a rash of substitutions breaking up the play, but finally Poland made the breakthrough when Grosicki clipped in a fine right-footed cross that Sobiech rose to flick past Dorosevs, who will have done his hopes of finding a new club no harm with an assured performance.
That sparked the Poles into a late surge of attacking play but they were unable to find a second and, with a minute of normal time remaining, Austrian referee Harald Lechner had seen enough and ended the encounter early.
Poland play Slovakia in their next Euro 2012 warm-up on Saturday, and they are expected to field a first-choice line-up for that clash.