Two tries from Scotland wing Sean Lamont and Welsh flanker Aaron Shingler were matched by Munster through Ireland lock Donnacha Ryan's and wing Simon Zebo's first-half efforts.
Zebo, who now has seven tries in the league this season, furthered his reputation as the coming man of Irish back play with his sharp finish in the 21st minute.
The draw scuppered Munster's hopes of earning a home semi-final but did rubber stamp their play-off place.
Elsehwhere young Welsh talent Matthew Jarvis broke Aironi hearts with an 80th-minute penalty at the Sportsground to help Connacht win 19-16.
Aironi were looking good for their first ever away win when at half-time when Azzurri pair Quintin Geldenhuys and Luciano Orquera established a 16-3 lead.
Geldenhuys played in all Italy's RBS 6 Nations matches this year and Orquera, who inspired Italy to their most famous Championship victory against France last year, showed new coach Jacques Brunel he still has the game to play for the national side with 11 points overall.
But the 21-year-old and former Wales Under-20 star Jarvis stole the game away from the Italians with his killer boot right at the death after replacement Rodney Ah You and fly-half Miah Nikora had brought Aironi level.