Tries in the final 15 minutes from Sean Maitland and Mako Vunipola saw Saracens eventually see off a stubborn Munster resistance in the Pool 4 clash in Allianz Park.
Munster, who lost captain Peter O'Mahony to injury in the warm-up, defended superbly for the first hour, frustrating the defending champions in a tense and occasionally bad-tempered game.
It was 3-3 at half-time and Munster made most of the running in the third quarter, JJ Hanrahan kicking the visitors into the lead early in the second half.
A rather serious looking melee, involving almost every player on the pitch, and apparently sparked by a row between Jamie George and a member of the Munster medical team, appeared to energise the home side.
A late surge from the hosts saw Maitland dive over in the corner following a powerful carry and offload by Billy Vunipola. Moments later, Vunipola would burrow over from close range to all but seal the win.
Munster had a chance to gain a losing bonus point but surprisingly opted to kick for the corner rather than the posts, a decision which failed to yield a try.
With two games left in the pool, it remains to be seen whether the visitors will rue this decision.
Ireland flanker O'Mahony pulled up with a groin strain during the warm-up and was replaced by Jack O'Donoghue before starting blindside Tadhg Beirne was carried off on a stretcher after falling heavily during a tackle in the 11th minute.
Up until Beirne's departure, Saracens only had an Owen Farrell penalty to show for their dominance and by the end of the opening quarter Munster had barely left their own half.
Billy and Mako Vunipola, Ben Earl and Alex Lozowski made early dents in the opposition and Farrell chose to send another kickable three points into touch for a line-out that amounted to nothing.
When Munster launched their first meaningful attack they built sustained pressure at short range and full-back Max Malins was forced to make a try-saving tackle on Andrew Conway.
The attack ended with a Harahan penalty but Saracens were straight back on to the front foot with Malins almost wriggling over, but there was a wobble before half-time as Farrell missed a routine penalty and Elliot Daly kicked the ball dead.
Munster were now tightening the screw and it was during this phase that the brawl erupted and once order had been restored, Harahan was given a shot at goal that he missed.
Tensions were rising and every victory on the pitch was celebrated wildly by players and fans alike and in the 66th minute Saracens made the breakthrough as reward for a sustained barrage on the whitewash.
Number eight Billy Vunipola broke from a five-metre scrum and after entangling a number of red shirts with his run, he popped out a pass over the top to Maitland to touch down.
Mako Vunipola then delivered the killer blow when he used his strength to power over from close range, ending Munster's resistance.
