Stephen Kelly went close for the Republic with a first-half header for the visitors, but substitute Lukasz Teodorczyk almost won it for the hosts in spectacular style with a long-range second-half strike.
But the Republic held on for a draw to go with their 3-0 victory over Latvia to leave O’Neill and assistant Roy Keane smiling at the end of their team’s first get-together.
O’Neill revealed after Friday evening’s game that he would use the trip to Poland to assess the depth of his squad, and he was as good as his word as he retained only four of the men who started at the Aviva Stadium.
One of them, Aiden McGeady, picked up where he had left off, running at the Polish defence in the early stages to pin the home side back.
The Spartak Moscow winger forced Piotr Celeban into an eighth-minute block which left the defender winded, and as front two Shane Long and Anthony Stokes made their presence felt, Ireland had marginally the better of the early stages.
They might have gone ahead with 21 minutes gone when, not for the first time, a set-piece almost paid dividends.
Jon Walters, wearing the captain’s armband in the absence of the rested Robbie Keane, flicked on McGeady’s corner and found Kelly unmarked in front of goal.
However, the full-back was unable to react quickly enough and although he managed to head the ball down, it reared up off the turf and looped over keeper Wojciech Szczesny’s crossbar.
Poland had caused few problems for the visitors up to that point, but they stepped up a gear as the half progresses with star men Lewandowski and Jakub Blaszczykowski starting to make an impact.
Keeper David Forde needed two attempts to claim Blaszczykowski’s 25th-minute shot as it skidded across the uneven surface, and defender Adam Marciniak lifted a header harmlessly over 11 minutes later.
However, Ireland largely managed to contain the tricky Lewandowski, although substitute John O’Shea – he had replaced the injured Sean St Ledger after just 31 minutes – was booked for deliberate handball after being caught out by the striker.
Blaszczykowski very nearly got the second half off to the perfect start for the Poles when he carved his way between Kelly and midfielder James McCarthy and into the penalty area, and he might have gone all the way had O’Shea not intervened at the decisive moment.
An off-balance Long skied a 51st-minute left-foot effort high over at the other end and Walters saw an ambitious attempt blocked by Marciniak two minutes later as Ireland responded.
Szczesny had to make a smart save on the hour to keep out Stokes’ well-struck effort after he had been picked out by McGeady, who departed soon afterwards along with McCarthy as defender Alex Pearce and James McClean joined the fray.
The Wigan winger needed just six minutes to make an impression with a teasing cross to which neither Long nor Stokes could get a touch in front of goal.
But fellow substitute Teodorczyk whistled a speculative effort over Forde’s bar seconds later with the game starting to open up.
Poland piled on the pressure as time ran down, but Forde had few saves of note to make with the men in front of him battling admirably to secure a shut-out.