Ireland stars Peter O'Mahony, Tadhg Beirne and Conor Murray all returned in what was a repeat of last May's United Rugby Championship final.
However, the poor weather conditions made for a cagey, defence-dominated contest, with Edogbo's try just before half-time punishing a yellow card for Stormers captain Neethling Fouche.
Jack Crowley converted, adding to his earlier penalty, for a 10-0 lead and Sacha Feinberg-Mngomezulu's 45th-minute penalty proved to be the South Africans' only score.
Despite the greasy ball, Munster exerted enough control to return to winning ways. The Stormers, though, have lost three URC games in a row for the first time.
John Dobson's side still have to welcome back their Rugby World Cup-winning Springboks but there were starts for international hooker Joseph Dweba and fit-again centre Feinberg-Mngomezulu in Limerick.
Sti Sithole jumped on turnover ball to spoil Munster's first maul attempt and a promising break by Evan Roos was halted by a Willie Engelbrecht knock-on.
O'Mahony pinched a lineout back on Munster's side and, when play moved infield, Crowley slotted over a 14th-minute penalty for the opening score.
Feinberg-Mngomezulu missed a long-range penalty before the Stormers' maul defence soon came up trumps again, with Roos and Ben-Jason Dixon getting the plaudits.
Munster failed to capitalise on breaks from Alex Nankivell and Shane Daly while Leolin Zas' dangerous run and kick chase was covered by Daly and Crowley.
The hosts crucially dominated play just before the interval and the Stormers' third successive maul penalty, near their own line, landed Fouche in the bin.
The 20-year-old Edogbo crashed over from a ruck at the end of eight battering phases. Crowley converted with the final kick of the half.
Ruben van Heerden's lineout steal early on the resumption, coupled with some improved carrying from his team-mates, set up Feinberg-Mngomezulu to split the posts from close range.
Veteran prop Stephen Archer then came on for his 268th Munster appearance, equalling Donncha O'Callaghan's record as their most-capped player of all-time.
An Engelbrecht turnover penalty thwarted a promising Munster spell while Roos was held up twice amid a series of scrum penalties where the Stormers really got on top.
Crowley and Murray's tactical kicking pinned the opposition back late on and even when Angelo Davids had some rare space to attack, Nankivell and Crowley swiftly slammed the door shut.