Maharoof's haul of four for 25 in 10 overs included a sensational start that saw the pace bowler take three wickets in four balls in his first over.
Off-spinner Muralitharan followed up with two wickets in three balls in his first over on his way to a miserly return of four for 19 in five overs.
Ireland's total - which featured five noughts - was the lowest at this World Cup, edging Bermuda's 78 against Sri Lanka.
The 1996 champions recalled bowlers Chaminda Vaas and Muralitharan, controversially rested for the seven-wicket defeat by world champions Australia here Monday when they were already through to the semi-finals, but it was Maharoof who sparked the slide.
The first change was pulled and driven through extra-cover for fours off his first two balls by Jeremy Bray, one of an all left-handed top five.
However, he then switched to round the wicket, and with his next delivery had Bray pushing a catch to Russel Arnold at short extra-cover leaving Ireland 28 for one in the eighth over.
Two balls later Andre Botha sparred outside off-stump and was caught behind by wicket-keeper Kumar Sangakkara for nought.
Next ball Eoin Morgan was brilliantly caught by a diving Sangakkara for a golden duck and Ireland were 28 for three with Maharoof on a hat-trick at the start of his second over which Niall O'Brien survived.
But Maharoof had a fourth wicket when opener William Porterfield (17) skied to Sanath Jayasuriya at mid-on.
Murali then struck with his second ball when Niall O'Brien was caught behind and two balls later postman Kenny Carroll, on his World Cup debut and the only change to the team that beat Bangladesh by 74 runs in Barbados on Sunday, missed a full toss and was bowled round his legs for nought.
Maharoof's fine day continued when he ran out Ireland captain Trent Johnston for nought after the batsman pushed the ball back and set off only for the bowler to throw down the stumps.
Kevin O'Brien and Kyle McCallan then both fell cheaply to Murali before Dave Langford-Smith, dropped on four, hit Maharoof for six.
Langford-Smith was last man out, lbw to Vaas for 18, the innings finished inside 28 overs.
This was Ireland's final match of the World Cup, the surpise package of the tournament starting the day seventh in the standings and unable to qualify for the semi-finals.
Their score was compiled against a Sri Lanka attack missing fast bowler Lasith Malinga, out for a third straight game with a left ankle injury.
Sri Lanka's next match is the first semi-final in Jamaica on Tuesday where their likely opponents will be New Zealand.
Ireland 77 all out in 27.4 overs (Bray 20, Langford-smith 18, Porterfield 17; Mahroof 4 for 25, Murali 4 for 19) Vs Lanka (yet to bat).