Harlequins gained revenge for last season's Heineken Cup exit, but they were made to battle all the way at the Sportsground in Galway by a brave Connacht side.
In the end, the class and experience of the Premiership champions secured a hard-earned win which keeps Quins top of Pool Three and on course for a quarter-final spot, with back-to-back matches against inexperienced Italian side Zebre to come in December.
These two sides managed only 17 points between them when they clashed in the wind and rain in Galway in January, but there were 43 points on the scoreboard by the interval on a dry evening here.
At one stage Connacht surged 10 points clear with the wind behind them, but Harlequins hauled them back and posted 15 points in the final 10 minutes of the opening half.
The English champions kept ball in hand and built the phases well, but Connacht, as Harlequins discovered when they were knocked out in January with that 9-8 result, can make the most of limited possession to frustrate their opposition. That was illustrated with a possession statistic after 14 minutes which showed Quins had 85 per cent of the possession – but still trailed 10-6.
Ben Botica continued his fine form from last weekend with a fifth-minute penalty but his side were rocked a minute later when Dan Parks put Dave McSharry through from 25 metres for a try which Parks converted.
The former Scotland player continued to direct operations for Connacht, putting his scrum-half Kieran Marmion away with another excellent line-break which yielded another penalty, as Parks made it 16-9 after 25 minutes after Botica had pulled back a couple of penalties for Quins in response to another Parks effort.
Fetu'u Vainikolo cut a good break through the Quins defence for a 28th-minute penalty opportunity which made it 19-9, and the home crowd warmed themselves up for another shock win.
But Quins didn't panic. They continued to build the phases, going lateral and making the hard yards and, inevitably, they got over on the half-hour when scrum-half Danny Care broke on the blindside off a scrum in the 22 to score.
They surged forward after that and while Jordan Turner Hall was held by a desperate home defence, Care sniped off the ruck to score his second try. Botica added the points from the conversion this time and also landed a penalty on the stroke of half-time to send them in 24-19 to the good.
Early second-half pressure saw Parks reduce the deficit to two with his fifth penalty. But Conor O'Shea's men refused to panic, and while their possession game rarely Botica extended the lead with a 50-metre penalty after 56 minutes to restore their five-point lead.
He pushed them outside of losing bonus-point territory for Connacht when he landed his sixth penalty of the night, this time from 45 metres, to make it 30-22 after 63 minutes, with their capitain Chris Robson leading the way as Quins closed out the game.
Connacht R Henshaw; T O'Halloran, E Griffin (M Fifita, 65), D McSharry, F Vainikolo; D Parks, K Marmion; D Buckley (B Wilkinson, 64), A Flavin (J Harris-Wright, 64), N White (R Loughney, 68); M Swift (E McKeon, 64), M McCarthy (N Kikora, 76); J Muldoon, W Faloon (J O'Connor, 57), G Naoupu.
Harlequins M Brown; T Williams, M Hopper, J Turner-Hall, S Smith; B Botica, D Care; J Marler, R Buchanan, J Johnson; O Kohn (C Matthews, 73, G Robson; M Fa'asavalu (T Guest, 67) , C Robshaw, N Easter
Referee Jerome Garces.
Pens: Parks 5
Tries: Care 2
Pens Botica 6