Conor O'Shea's men became just the second team to beat Munster in a European match at the Limerick venue, following up on Leicester's Heineken Cup pool win here in January 2007.
First-half tries from George Robson and Danny Care (pictured) set the tone for Quins, who will face Stade Francais in the Amlin Challenge Cup final in Cardiff on May 20.
Winners of this competition on two previous occasions, the Londoners were outstanding in the opening half-hour, controlling play and winning the collisions.
Nick Evans missed two penalty efforts and Munster closed the gap to 14-7 by half-time, putting Felix Jones over for a relieving try in the last minute.
Paul O'Connell made his return from an ankle injury in the second half, yet Quins stood up to anything thrown at them and, helped by two Rory Clegg penalties, they held on despite having Nick Easter sent off for two yellow cards.
The visitors ratcheted up the pace early on, getting their offload game going under the direction of Danny Care and Evans. Maurie Fa'asavalu also levelled Keith Earls with a bone-crunching tackle.
The visitors dominated possession and territory in a frenetic opening salvo, Evans sending a delicious wide ball to send Gonzalo Camacho slaloming past Paul Warwick and Doug Howlett. He was hauled down close to the try-line but Quins swiftly moved the ball wide to the right, where lock Robson dived in past James Coughlan.
Evans topped off the ninth-minute try with a well-struck conversion and the Londoners' early barrage continued with the forwards regularly crossing the gain line. A crucial intervention from O'Gara prevented George Lowe from getting over in the left corner.
Good pressure from Earls on Camacho yielded a scrum for Munster in the visitors' 22. However, the covering Monye foiled a back-line move involving Felix Jones.
Two muddled Munster lineouts invited Fa'asavalu to take on O'Gara and company, but Evans dragged a penalty to the left and wide after a high tackle from Wian du Preez.
The New Zealander had another uncharacteristic miss in the 29th minute, failing to punish Munster for hands in the ruck, and took a worrying knock to his left knee as Quins maintained their attacking poise.
Having received medical attention, Evans almost wormed his way over close to the posts. From the next ruck, Munster's overworked defence was caught out by Care's feint and stretch for the line.
The England scrum-half had enough downward pressure with his fingertips to satisfy television match official Giulio De Santis, with Care adding the conversion himself.
O'Gara turned down a kickable penalty as Munster went in search of their first points late on. Their endeavour was rewarded when Lifeimi Mafi and Warwick straightened for Jones to come in on an angle and glide over from close range. O'Gara landed the conversion to give Munster a further boost.
Replacements O'Connell, John Hayes and Sam Tuitupou helped Munster up the tempo on the restart, Quins introducing youngster Clegg for the injured Evans.
Donncha O'Callaghan and Easter earned time in the sin-bin for scuffling off the ball, before Clegg coolly slotted a right-sided penalty for Quins in the 50th minute.
O'Shea's side threatened again with ball in hand, Munster needing a clever piece of play from Denis Leamy to keep their defence intact.
There were near misses for Lowe and Howlett, the latter having a try ruled out for a forward pass from Jones. Another forward pass prevented Howlett from scoring and O'Connell was held up close to the line.
Mike Brown was alert to cover a chip-and-chase from Howlett, who got over for a deserved try in the 78th minute. A ruck offence had seen Easter walk eight minutes earlier, and the former All Black struck from close range to give Munster late hope.
But O'Gara's conversion attempt from wide out on the right was off target and Harlequins' heroic defence, led by captain Chris Robshaw, was rewarded at the final whistle.