Roberto Mancini's men looked to be heading for a disappointing stalemate due to poor finishing but Biraghi bundled in from close range in stoppage time to set up an intriguing League A Group 3 contest with pacesetters Portugal in November.
Italy were completely dominant in the first half but somehow failed to take the lead, with Jorginho and Lorenzo Insigne both hitting the crossbar.
Poland made a marked improvement in the second period, though Italy remained the controlling force and finally clinched a deserved three points right at the end, moving them to within two points of Portugal.
IT'S ALL OVER #PolandItaly 0-1— Italy (@azzurri) October 14, 2018
What drama!! Italy dominate over in #Chorzow and secure an extremely late win thanks to a goal from #Biraghi at the death. #POLITA #VivoAzzurro #NationsLeague pic.twitter.com/dZoOIXwIGw
It did not take Italy long to establish control and they almost opened the scoring in the second minute, as Jorginho struck the crossbar from 25 yards.
Poland had another lucky escape after half an hour – Insigne prodding Federico Bernardeschi's cross onto the frame of the goal.
Italy's dominance only increased as half-time approached, but the breakthrough eluded them due to the heroics of Wojciech Szczesny, who produced fine saves to deny Jorginho, Alessandro Florenzi and Giorgio Chiellini.
The hosts looked more solid after the break and finally tested Gianluigi Donnarumma just before the hour, with the goalkeeper thwarting Kamil Grosicki from a tight angle.
Shortly after Bernardeschi headed wide from close range, Donnarumma again had to be alert, parrying another Grosicki effort away and then seeing Arkadiusz Milik blast the rebound over.
It was ultimately Italy who took the spoils, however, as Kevin Lasagna flicked on a corner delivery and Biraghi nudged it over the line from close range.
The result sees Poland become the first team relegated to League B.
What it means: Promising signs for Mancini
Italy's wastefulness in front of goal is something that can certainly be improved, but in terms of their general play in Chorzow, Mancini's side played some attractive and entertaining football. Tweaks may be needed, but there is definitely life in them.
Szczesny's efforts go to waste
Were it not for the Juventus goalkeeper, Italy could have been comfortably ahead at half-time. Szczesny made a string of smart saves when those ahead of him failed to end the danger, but he was helpless for the winner.
Chiesa flatters to deceive
While Bernardeschi was hardly impressive, he was at least involved and an occasional threat – Federico Chiesa was not, and he barely made an impact in attack. A disappointing display.
Poland face Czech Republic in a friendly on November 15, before travelling to Portugal for their final League A Nations League game five days later. Italy's last match in the competition sees them host Fernando Santos' group leaders on November 17.