Harlequins booked their place in the final of the Parker Pen Challenge Cup despite a second-leg loss to Connacht.
Connacht 23 (10)
Tries: Yapp, Elwood
Cons: McHugh (2)
Pens: McHugh (2)
Harlequins 18 (10)
Tries: Burke, Greenwood
Pens: Burke (2)
Quins had gone into the game with a nine-point lead and looked on course for an easy win when Paul Burke's converted try put them 10-3 ahead.
Tries from David Yapp and Eric Elwood plus the boot of Mark McHugh edged the home side into a four-point advantage over the two legs.
But Quins centre Will Greenwood sealed victory with a 66th-minute try.
Connacht barely looked capable of competing early on as they struggled to contain their opponents' exciting runners.
But, after Burke's penalty and converted try, they deservedly levelled in the 25th minute after a passage of sustained pressure.
Michael Walls spread it to Elwood, who popped it in for the in-coming Yapp. McHugh duly converted the score, adding to an earlier penalty.
Harlequins' two-leg advantage was reduced to just six points straight after the re-start with a quick-fire Elwood drop goal.
And Elwood then moved his side in front in the 56th minute, leaving the opposition defence in disarray and beating the clutches of three tacklers to the line.
The visitors hit back when Greenwood bundled his way through a melee of Irish defenders to put his side a point clear over the two legs.
Burke then had two chances to stretch the lead, missing the first - an attempted drop-goal - and making no mistake with the second - a simple penalty.
Despite eight minutes of added time, Quins held on and will face French side Montferrand in the final.
Connacht: Mostyn; McPhillips, Yapp, McHugh, Munn; Elwood, Walls; McFarland, Jackman (capt), Bracken; Browne, Farley; Swift, Lacey, O'Sullivan.
Replacements: Fogarty, Clarke, McCarthy, Neville, O'Loughlin, Moore, Robinson.
Harlequins: Duffy; Harder, Greenwood, Deane, Monye; Burke, Keogh; Jones, Hayter, Dawson; Rudzki, Miall; Sanderson, Vos, Diprose (capt).
Replacements: Dott, Gomez, Worsley, Davison, Sherriff, Willis, Dunne.