Pizarro joined Nicola Cattina on the first-half scoresheet as their lead slowly dwindled throughout the second half courtesy of Ian Keatley's boot, a penalty try and Lifeimi Mafi's late effort.
Reigning champions Munster's only previous loss in their last ten matches was 17-33 reversal at Ulster in December and having won all three previous meetings with Aironi coach Tony McGahan welcomed back David Wallace for the first time this season after a serious knee injury.
But it was Pizarro who was to steal the headlines in this rearranged fixture and in doing so staked a claim for a first-team place in coach Rowland Phillips' first team.
With ten players away on international duty, Phillips made five changes to the side that lost 22-6 against Leinster last Friday but it was the visitors who missed an early opportunity to take the lead when Scott Deasy failed to convert a fifth-minute penalty.
They were made to pay when Cattina ran in for the hosts two minutes later. The 26-year-old flanker saw his try go unconverted by Luciano Orquera but the fly-half made up for it when he kicked a penalty on 14 minutes to give the Italians the early initiative.
Deasy slotted home his next opportunity just before the half-hour mark but their inability to cross the line came back to haunt them again when Pizarro went over for Aironi two minutes before the break.
The centre picked up a neat Matteo Pratichetti pass to burst through Munster's line and extend his side's lead to 15-3 at half-time.
Orquera added another three points after the restart but the Irish province were given a lifeline on the hour when they were awarded a penalty try after strong work in the scrum was illegally halted in front of the posts.
Replacement Keatley converted to reduce the deficit to eight points before Orquera responded again with a penalty, this time from long-range.
The Munstermen were not going to lie down though, and Mafi brought the scores to within a converted try with his 74th minute effort as Keatley's second conversion of the game made it 21-17 to set up a frantic last five minutes.
However, despite a number of concerted efforts, the Irish side could not break down the determined Aironi defence who held on for a valuable victory.
|Aironi Rugby Score Card|
|Munster Rugby Score Card|