The Scottish outfit's passage was secured by tries from Tim Visser, Jim Thompson, Netani Talei and Lee Jones, plus a string of kicks from captain Greig Laidlaw, who landed all four conversions and a brace of penalties.
The Exiles, who had no chance of progressing from Pool Two, posed a limited offensive threat. Their points came from a Jonathan Joseph try and two penalties by Adrian Jarvis.
Edinburgh dominated the early proceedings but the closest they came to breaking through was when Laidlaw sent through a speculative chip and Matt Scott was beaten in the race to the line.
There were almost six minutes on the clock when Irish had their first visit to Edinburgh territory. That venture yielded a penalty which Jarvis steered between the sticks to nudge his side ahead.
The lead lasted only two minutes as Laidlaw gathered at the breakdown and slotted a kick between two opposition defenders. The ever-alert Visser - operating on the 'wrong' wing - won the sprint to the line and Laidlaw added the extra two points from wide on the right.
The skipper extended the Scots' lead with a close range penalty following an offence at a scrum with 20 minutes played, but that was swiftly nullified by a Jarvis effort.
However, Edinburgh were soon back on the offensive and, when Irish strayed offside 25 metres from their posts, Laidlaw added three more points to the home tally.
Four minutes before the interval, the home side earned further reward for their dominance when, after a series of phases which carried them to within two metres of the line, the ball was moved wide and Laidlaw fired out a pass that found Thompson in space.
The full-back raced over untouched and the immaculate boot of Laidlaw added the conversion to send Edinburgh in at the break with a 20-6 advantage.
Irish showed greater urgency after the restart but, despite almost 10 minutes of uninterrupted possession and numerous phases of play, they were easily repelled.
The visitors sought to liven up their challenge with an infusion of fresh blood and twice tried but failed to unleash the pace of Delon Armitage. But the Edinburgh line remained intact.
Having spent almost 20 minutes on defensive chores, the hosts launched a fresh assault when Roddy Grant burst through and offloaded to Scott. He in turn sent Visser scampering in at the corner - only for the referee to call back play after adjudging Grant's pass forward.
Irish responded with a rare flash of urgency. Ross Samson's quickly taken free-kick allowed Joseph to race down the flank and exchange passes with Adam Thompstone, taking the return and powering past two defenders for an unconverted score that left Edinburgh 20-11 ahead with 14 minutes to play.
However, Edinburgh were not to be denied and another spell of sustained pressure created the platform for the ball to be moved wide to the lurking Talei, who was on hand to crash over.
Edinburgh set off in pursuit of the bonus point score, which came with three minutes to spare when Lee Jones raced down the right flank to score. Laidlaw maintained his unblemished form with the boot.
The joy in the record Murrayfield Heineken Cup crowd was enhanced by the news that Cardiff had failed to secure a bonus point victory, handing the Scottish side home advantage in the quarter-finals.
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