Munster outscored the South Africans three tries to two to snatch the title, having finished fifth in the regular season standings but winning away in the quarter-final, semi and final to take the trophy.
The Irish side dominated early proceedings at the Cape Town Stadium but in the second half were under intense pressure before breaking the stranglehold to score the decisive try.
Munster, who had upset top-ranked Leinster in the semi-final, were strong from the kickoff in wintery conditions but fell behind when Stormers flyhalf Manny Libbok intercepted in his own half to streak away for the opening try of the game in the sixth minute.
The Irish replied within four minutes with a pushover try from hooker Diarmuid Barron.
Munster then crossed over three times but on each occasion had the score disallowed - first when Gavin Coombes made an illegal second movement to stretch over the line, then for a knock-on as Antoine Frisch crossed and for a forward pass as Mike Haley went crashing through.
But Munster’s dominance was rewarded with a superb crosskick from flyhalf Jack Crowley that bounced perfectly for Calvin Nash to score in the 29th minute and put Munster 12-7 up at halftime.
The Stormers returned from the break with much more intent and a powerful maul allowed veteran loose forward Deon Fourie to go over with Libbok’s conversion putting the hosts back 14-12 ahead in the 50th minute.
An attritional contest, without any score, followed for the next 25 minutes before Munster suddenly burst into the home half and Hodnett crashed over in the corner for the win.
"We performed well in the first half and we could have been a couple of scores (ahead) but the Stormers' defence was excellent," said winning captain Peter O'Mahony.
"Then we were down and there was 20 minutes of to-ing and fro-ing with incredible defence then with five minutes to go we showed incredible resilience and skills to score a well-worked try on a poor surface, a great try to finish it off. We stuck to our guns. The last five minutes there, class," he added.
The Stormers had won last year in the first year of participation by South African sides in the competition previously called the PRO-14 with Irish, Italian, Scottish and Welsh clubs.
