The Eagles were second best in a game of few clear-cut goalscoring opportunities at Stadium 974, but they were presented with the best chance to win the match just before the hour mark when Lewandowski was pulled down inside the area by Hector Moreno.
However, the Poland captain was denied his first-ever goal at the World Cup by Mexico skipper Guillermo Ochoa, who dived to his left to keep the score level.
Both nations were eventually forced to settle for a share of the spoils and failed to take full advantage of the earlier result in Group C which saw two-time world champions Argentina suffer a shock 2-1 defeat against Saudi Arabia, who against all odds finish the evening top of the group.
It was Mexico who started the brightest and the first chance was created down the right flank by Hirving Lozano, who whipped a cross with real place towards Alexis Vega rushing in at the back post, but the attacker was unable to direct a decent effort on target.
The Mexicans were riding on an adrenaline wave created by their raucous supporters, and they looked the most likely to break the deadlock, while Poland were content to sit back and allow El Tri to spray the ball around in the hope they could intercept and catch them on the break.
Indeed, the Eagles were cagey and offered little going forward in the first half, with Lewandowski kept quiet by Mexican trio Moreno, Cesar Montes and Edson Alvarez.
The best chance of the first half fell to Mexico in the 26th minute when Hector Herrera dinked a cross from the right channel into the Poland penalty area towards Vega, who outjumped Matty Cash and floated a header narrowly wide of the far post.
Nine minutes after the break, a half-chance fell to Lewandowski who burst into the area between Montes and Moreno, before going to ground following a challenge from the latter.
Australian referee Chris Beath initially waved the incident away, but VAR intervened and advised the on-field official to take another look at the pitchside monitor, which showed Moreno holding a fistful of Lewandowski's shirt.
The referee eventually pointed to the spot and Lewandowski was the man to step up from 12 yards, but 37-year-old Ochoa - competing at his fifth World Cup - guessed correctly and dived to his left to deny the Barcelona striker's tame effort.
Wojciech Szczesny was then called into action in the 64th minute, with the Poland stopper at full stretch to deny Alvarez's audacious effort from around 35 yards that took a wicked deflection off Vega's head.
With 20 minutes remaining, Mexico called on Wolverhampton Wanderers striker Raul Jimenez - who had been suffering from a groin injury since the end of August - to play up front alongside Vega, who posed the biggest threat in the final third for El Tri.
While both nations were keen to snatch a late winner, they were also determined to avoid defeat in their World Cup opener, and the contest's enthusiastic tempo gradually dropped before the full-time whistle blew.
Mexico will now turn their attention to Saturday's encounter against an out-of-sorts Argentina outfit, which will take place a few hours after Poland lock horns with high-flying Saudi Arabia.