The Barcelona striker was generously awarded the chance to net his first World Cup goal - referee Chris Beath awarding the spot-kick following a VAR check - but was denied by Mexico goalkeeper Guillermo Ochoa.
Poland offered little else in a bitty encounter with Mexico, roared on by a boisterous support at Stadium 974, far more fluid going forward, particularly down the flanks.
Mexico offered the greater threat in the first half with Hirving Lozano predictably proving their main attacking outlet.
The Napoli winger created the first chance of note after five minutes, his curling cross from the right eluding Wojciech Szczesny but Alexis Vega was unable to turn the ball home at the far post.
In a rare Poland foray shortly afterwards, Lewandowski set Jakub Kaminski free but Mexico defender Jesus Gallardo did superbly to get back and smuggle the ball to safety.
Vega came close again after 26 minutes with a header that drifted inches wide while, on the stroke of half-time, Szczesny bundled Jorge Sanchez’s cross-shot over the bar.
The second half started in a similar vein with Mexico dominating possession but its over-confidence almost cost them. Edson Alvarez dallied on the ball and it ricocheted into the area where Hector Moreno and Lewandowski wrestled before falling to the turf.
Beach initially waved play on but then pointed to the spot after consulting the monitor with replays showing Moreno had a hold of Lewandowski's shirt.
Ochoa, so often Mexico's hero at a World Cup, came up trumps again, however, diving to his left to palm Lewandowski's spot-kick to safety.
The let-off failed to inspire Mexico who huffed and puffed without really testing Szczesny, bar a routine save to deny a flicked header from Henry Martin.
