One of the province's former back rowers, Nick Williams, scored a late consolation try for Aironi, who gave another good account of themselves.
Munster now hold a nine-point lead at the top of the table with six rounds remaining in the regulation phase of the Magners League.
Bottom side Aironi, who had lost their previous 14 league games, could have been in front at the break. Their Kiwi out-half James Marshall missed three penalties in the first half, two of which were eminently kickable.
Munster's Paul Warwick converted kicks after 5 and 20 minutes, the second in response to Marshall's only successful effort in the 12th minute.
The visitors, who lost in Treviso recently, had flanker Ryan sin-binned on the half hour mark, and put up a defensive wall while down to 14 men.
There were few scoring chances in open play - young winger Simon Zebo was called back for crossing as he jetted through - and the first try, in the 48th minute, came from a loose lineout throw.
Two minutes into the second half, Aironi winger Giulio Toniolatti was sin-binned for taking Warwick out in the air. A knee injury forced Denis Hurley off, and the Meath man could be looking at a lengthy spell on the sidelines.
The Italians then blundered as hooker Tommaso d'Apice's miscued his throw to the tail of the lineout and Ryan gobbled it up to go over unopposed for a seven-pointer.
Toniolatti had only just returned when Aironi flanker Gareth Krause was flashed a yellow card for not rolling away after a tackle.
Munster, who worked hard at set piece time, put the squeeze on the Aironi scrum and forced them to concede a penalty try which Warwick converted for a 20-3 lead.
With 23 minutes remaining, a now dominant Munster had time to go in search of further tries, but the final quarter was broken up by substitutions and some patternless play.
Williams, who was thwarted in the first half, had the final say for Rowland Phillips' side, driving over from close range with two minutes remaining. Replacement Riccardo Bocchino converted to cut the gap to 10 points, but the losing bonus point never looked on.
Speaking afterwards, victorious coach Tony McGahan said: "It's never easy to come away from home and win. We had a job to do and I'd be happy with the way we went about our business.
"Of course there are aspects we need to look at, but right now, I'd be more than happy with our day's work and the four points we're going home with."
Munster host the Newport Gwent Dragons next Saturday, in the first of two successive matches against Welsh opposition. Aironi, meanwhile, are Ireland-bound with trips to Ulster and Connacht over the next two Fridays.
|Aironi Rugby Score Card|
|Munster Rugby Score Card|