With coach Roberto Mancini isolating after testing positive for COVID-19, his team turned in an accomplished display in Reggio Emilia as it extended its unbeaten run to 21 matches.
Jorginho's 27th-minute spot-kick proved crucial, with the penalty awarded for Grzegorz Krychowiak hauling down Andrea Belotti, whose earlier venture into an offside position had cancelled out Lorenzo Insigne's would-be opener.
Though Belotti and Nicolo Barella squandered chances to add to Italy's lead, Poland's comeback hopes all but ended when Jacek Goralski received a second yellow card, with Berardi subsequently adding gloss to a dominant display.
Italy thought it had its reward for a bright start when Insigne drilled in from Barella's cross, only for the goal to be disallowed due to Belotti's position.
Yet the striker swiftly made amends by drawing a clumsy foul from Krychowiak, with Jorginho coolly sending Wojciech Szczesny the wrong way.
Belotti looked set to double Italy's lead only to volley over after latching onto Insigne's delightful pass, while Barella lashed over following the restart.
Goralski was fortunate to escape with a booking for a lunge on Belotti, with Poland's half-time substitute having flown in with his studs up, though his luck soon ran out.
After Belotti had a penalty appeal for handball dismissed, the Torino player was scythed into by Goralski, who duly received his marching orders to end a dismal cameo off the bench.
Italy made its numerical advantage count to grab a deserved second – Insigne playing in the unmarked Berardi to thump in his second international goal.