Roberto Mancini's men will not be at the World Cup in Qatar after a play-off defeat to North Macedonia, and they looked on course for another embarrassing loss here as Ardian Ismajli nodded Albania in front.
But Italy hit back almost immediately through Di Lorenzo, before Grifo added goals either side of half-time to secure victory.
It is now three straight wins for the European champion since its humiliating 5-2 thrashing at the hands of Germany in June, as it looks to bounce back from its FIFA World Cup disappointment.
Italy started brightly, but it fell behind when Ismajli rose highest to meet Nedim Bajrami's free-kick, sending a sublime header crashing into the top right corner.
Albania's lead lasted just four minutes, as Grifo's pinpoint cross picked out Di Lorenzo in the middle to side-foot home.
Creator turned finisher for Italy's second, Giacomo Raspadori squaring for Grifo before the Freiburg man smashed superbly past Etrit Berisha to make it 2-1.
Nicolo Zaniolo hit the base of the post in first-half injury time as Italy looked to build their lead, though Albania clung on to get into the break just a goal behind.
Marash Kumbulla's header shortly after the interval tested Alex Meret, while Grifo nearly scored his second when he lashed the underside of the crossbar.
Albania then hit the woodwork twice themselves, Myrto Uzuni's looping effort beating Meret but not the upper frame of the goal before Bajrami saw a shot deflected onto the bar.
Grifo made it 3-1 after 64 minutes, controlling a cross and dispatching into the far corner to round off the scoring and cap his sensational display.