Ben Healy kicked 14 points on his first European start to guide Munster past Castres in a scrappy contest at Thomond Park.
Jack O'Donoghue's second half try gave the hosts the breathing space they craved having controlled the game throughout while failing to pull away.
With three minutes left Kevin Kornath crashed over for Castres to set up a tense finish.
However the hosts held on to make it two wins from two in the competition.
Castres' hopes of a place in the last 16 now hang by a thread having lost both of their matches so far.
The win for Munster was a satisfying end to a tumultuous week in which head coach Johann van Graan announced he was leaving at the end of the season, before agreeing to join Bath for the start of the 2022-23 campaign, while fly-half Joey Carbery underwent elbow surgery for an injury sustained against Wasps last weekend.
The victory was secured in spite of a dysfunctional performance in which the hosts failed to bring the usually boisterous Limerick crowd into the contest.
Healy, stepping in at fly-half in place of Carbery, displayed typical accuracy with the boot to put his side nine points up in the first half before Damian de Allende spurned a gilt-edged chance to score the game's first try - opting to crash over himself instead of playing in team-mates out wide, but knocking the ball on as he attempted to ground.
Castres barely set foot in Munster's 22 in the first half and only registered their first score via the boot of Benjamin Urdapilleta in the final minute of the opening 40.
The French side's lack of attacking threat perhaps allowed Munster to remain in control of the contest even when they were struggling to create momentum themselves, but they saw enough of the ball to eventually carve out an overlap on the right that was powerfully finished by O'Donoghue in the corner.
Only then did Castres push forward meaningfully, with their first drive into the 22 repelled by a brilliant Tadhg Beirne turnover before Kornath drove between the posts minutes later to put his side back in the game.
However despite winning possession inside their own half with the clock in the red, the visitors settled with Urdapilleta kicking the ball dead to ensure his side would at least take home a losing bonus-point.
Munster: Campbell; Conway, Farrell, de Allende, Earls; Healy, Murray; Kilcoyne, Scannell, Ryan, Klein, Beirne; O'Mahony, Hodnett, O'Donoghue.
Replacements: Baron, J Wycherley, Knox, Jenkins, O'Sullivan, Casey, Crowley, Kendellen.
Castres: Larregain; Guillemin, Combezou, Aguillon, Nakosi; Urdapilleta, Arata; De Benedittis, Ngauamo, Hounkpattin, Jacquet, Hannoyer; de Crespigny, Meka, Kornath.
Replacements: Humbert, Nostadt, Guillamon, Whetton, Li Williams, Kockott, Le Brun, Zeghdar.