In what was a back and forth game, the home side came out on top 25-23.
Stander's try was the only one of the game for the hosts, as out-half Ben Healy hit four penalties to keep them in touching distance.
FULL-TIME: Munster 25-23 Edinburgh
It's another fantastic late show from Munster as CJ Stander's late try is converted by Ben Healy for a great #GuinnessPRO14 win!
Healy also kicked six penalties!#MUNvEDI #SUAF 🔴— Munster Rugby (@Munsterrugby) October 10, 2020
Earlier in the day, Leinster made it two wins from two after beating Benetton 37-25 in Treviso.
Tries from James Tracey, James Lowe and Ross Moloney gave Leinster a bonus point win away from home.
Full-time! A brilliant, hard-fought bonus-point win in Treviso!#BENvLEI #GuinnessPRO14 pic.twitter.com/lYwsUZoUa7
— Leinster Rugby (@leinsterrugby) October 10, 2020
Meanwhile, 14 men Ulster saw off Ospreys to win 24-12 as Iain Henderson was shown a red card late on for making contact with the head.
Tries from Jacob Stockdale, Marcel Coetzee and John Cooney gave Ulster their second win of the season as well.
𝙁𝙐𝙇𝙇-𝙏𝙄𝙈𝙀
Ulster make it two from two in the @PRO14Official with an excellent victory away from home! #OSPvULS #GuinnessPRO14 #SUFTUMLive ⚪️🔴 pic.twitter.com/iWc8v9OV2W— Ulster Rugby (@UlsterRugby) October 10, 2020
Connacht meanwhile had a tough day at the office losing 29-7 away from home against Cardiff Blues.
It took the away side 55 minutes to get on the score sheet as Conor Oliver crossed over to make the score 10-7 to Cardiff.
From there the home side scored three tries in a row, as Connacht could not deal with Cardiff's power.
Things do not get any easier for the men from the west as they travel to Edinbrugh next time out on October 25th.