Not for the first time this season, Harlequins had former All Black fly-half Nick Evans to thanks for extending their remarkable run of consecutive wins to 11.
Evans kicked 20 points via six penalties and a conversion, but no side to date this season have tested Quins more, to their immense credit in a cracking Heineken Cup, Pool Six tie.
Having established a record unbeaten run from the start of a season by a top-flight club at Bath last weekend, Harlequins were very keen to stretch that to read win No 11 on 11-11-11. And it was the ruthless Evans who got the scoreboard ticking with a penalty after only five minutes. Connacht fly-half Miah Nikora equalised in kind two minutes later only for Evans to restore the home team's advantage with 10 minutes on the clock.
However, there was little about Connacht's busy beginnings to suggest that the first Heineken Cup tie in their history was in any way daunting.
And there was a very classy hue to their first try in Europe's premier competition on 13 minutes. It was created by a fine carry from Mike McCarthy,a darting break by Eoin Griffin opened up the defence and his precise pass to his left was snaffled gleefully by Tiernan O'Halloran who scored in style, Nikora adding the conversion.
After Evans added a third penalty Harlequins stretched the Irish defence, first to the right and then across to the far wing. Getting numbers to the repeated breakdowns was increasingly difficult for the visitors and Karl Dickson picked up behind a ruck, dummied to pass right but darted through a gap to score from six yards with Evans converting.
Evans did what he does best with two minutes of the half remaining, firing over a penalty for a high tackle on Joe Marler by Thomas Anderson – son of the famous Willie.
Connacht reversed the flow of the game from the restart, and their intense pressure was rewarded on 57 minutes with a fine try on the left scored by former Harlequin Gavin Duffy and converted by Niall O'Connor.
Evans eased the pressure five minutes from time, climbing off the ground after taking a bang on the head to steer a penalty between the posts, and he finished off the brave visitors with his seventh kick from eight attempts with two minutes left.
Harlequins: Try Dickson; Con Evans; Pens Evans 6.
Connacht: Tries O'Halloran, Duffy; Cons Nikora, O'Connor; Pen Nikora.
Harlequins: M Brown; S Stegmann, G Lowe (B Urdapilleta, 34), J Turner-Hall, S Smith; N Evans, K Dickson (D Care, 49); J Marler, C Brooker (J Gray, 59), J Johnston, O Kohn (T Vallejos Cinalli, 14), G Robson, M Fa'asavalu (L Wallace, 73), N Easter, C Robshaw.
Connacht: G Duffy; B Tuohy, E Griffin, D McSharry (H Fa'afili, 66), T O'Halloran; M Nikora (N O'Connor, 48), P O'Donohoe (F Murphy, 54); B Wilkinson (R Loughney, 69), A Flavin (E Reynecke, 54) R Ah You (D Rogers, 54), M Swift, M McCarthy, J Muldoon, G Naopupu, R Ofisa (T Anderson, 27).
Referee: J Garces (France).