Edinburgh's European hopes appear over after Sunday's defeat by Munster left last season's semi-finalists with no points from two Pool One fixtures.
Munster sealed the bonus point just as the match was entering stoppage-time when hooker Damien Varley got over for the fourth try in Limerick.
The earlier tries had come from scrum-half Conor Murray and forwards Peter O'Mahony and Sean Dougall.
Fly-half Ian Keatley kicked the other 13 points for the two-times winners.
It was Munster's first win of the campaign after an opening defeat by Racing Metro, and the emphatic result means Edinburgh have conceded 78 points and not scored any in their two matches.
There looks no way back for Michael Bradley's side in the competition now with this defeat coming a week after they were humiliated 45-0 by Saracens at Murrayfield.
The visitors were right in conention at the interval, trailing only to Keatley's two successful penalties from four attempts.
But scrum-half Murray's try, confirmed after lengthy consideration by television match official Geoff Warren, saw the Irish province pull away.
An alert Murray spotted a gap in the Edinburgh defence and just about made the line under the posts.
Another Keatley penalty made it 16-0 before three tries in the closing 10 minutes.
After a line-out, the Munster pack summoned a charging drive which carried O'Mahony over the line in the 71st minute and Keatley converted for 23-0.
The impressive Keatley almost added a try himself but was halted just short of the line. Flanker Dougall, however, was there in support and dived over for the third try.
The home fans roared the men in red on in the last few minutes and they snatched the extra point through Varley.
Munster: Hurley, Howlett, Laulala, Downey, Zebo, Keatley, Murray, Kilcoyne, Sherry, Botha, D. O'Callaghan, O'Connell, D. Ryan, Dougall, P O'Mahony.
Replacements: Jones for Howlett (65), Hanrahan for Downey (73), Horan for Kilcoyne (80), Varley for Sherry (63), Butler for D O'Callaghan (73), Holland for O'Connell (61).
Not used: Archer, Williams.
Edinburgh: Tonks, Jones, De Luca, Atiga, Brown, Hunter, Rees, Yapp, Ford, Cross, Gilchrist, Cox, Denton, McInally, Talei.
Replacements: Scott for Atiga (13), Fife for Hunter (64), Hislop for Yapp (76), Titterrell for Ford (76), Nel for Cross (41), McAlpine for Cox (75), Basilaia for Talei (52).
Not used: Leck.
Ref: Wayne Barnes (England).
Munster coach Rob Penney: "The bonus point could be very important. The critical thing is we have a couple of massive games pre-Christmas against Saracens.
"We are still masters of our own destiny in that regard. If we do well then we are still in the hunt, whether we get bonus points or not.
"The performance today probably wouldn't be good enough to beat Saracens. We still have lots and lots to do.
"The most pleasing thing about this win was the way the boys embraced their work and got into it, they were hurt after last week [against Racing Metro]. We still have a lot of improving [to do]. Our unforced error rate was far too high.
"Edinburgh were hurting as well and for the first half it was a competitive match. I felt we dominated territorially for large parts and controlled the fixture to that point, but we hadn't capitalised or got the rewards."
Edinburgh coach Michael Bradley: "At this stage you won't be saying 'no' to qualifying for the quarter-finals, if we win the last four games and get four bonus points and scrape in as the number eight qualifier, which is very unlikely.
"Losing your first two games and getting no points is a recipe for being out of the competition. You have to acknowledge that.
"We are not necessarily worried about winning the Heineken Cup or the Amlin Challenge Cup now, we are more worried about winning the next [league] match against the Scarlets at this stage."