Connacht did more than enough to see off Cardiff at Dexcom Stadium in Galway to advance to the last eight in the Challenge Cup.
And they will be at home again next Saturday night as they bid to reach the semi-finals of the competition for the first time in 15 years when they host Racing 92.
Mack Hansen led the way as Connacht held off a Cardiff side they had already beaten twice since January.
Connacht, with 60% possession, led 14-8 at the break after finishing the opening half with a flourish despite having Hansen in the bin.
They started the game in similar fashion, taking the contest to a Welsh side they have defeated home and away in the past eleven weeks, and on a perfect night for rugby in Galway, they hit the front after less than three minutes.
The score came from livewire scrum-half Matthew Devine after Sean Jansen had made the initial break and Hansen made inroads before feeding his scrum-half who got through two tackles to score.
JJ Hanrahan added the conversion for a perfect start but Connacht struggled to build on it despite plenty of possession and opportunity.
Cardiff hit back and Callum Sheedy got them off the mark with a penalty after 13 minutes in front of the posts. Cardiff, with James Botham and Taulupe Faletau prominent, pushed on from there.
Hansen was binned for killing the ball after a good break by Faletau, but when Cardiff tapped and went in front of the posts, they knocked-on and the opportunity was lost.
The reprieve did not last long for Connacht as Cardiff simply ran it through the numbers with a good pass from Sheedy key to a move which was finished in the right corner by Ray Lee-Lo for an unconverted try two minutes from the interval.
Connacht rallied before the break, opting for the corner from a kickable penalty and they were eventually rewarded just when it seemed Cardiff had done enough to contain them but lock Josh McNally again offended and was binned.
This time Connacht made it count with the clock four minutes in the red when Jansen found a way through and Hanrahan converted to give them a 14-8 interval lead.
They pushed that lead out to 21-8 two minutes after the restart when tighthead Finlay Bealham and hooker Dave Heffernan displayed super pace to send Finn Treacy away for a fine try, which he took in behind the posts for Hanrahan to convert.
Cardiff hit back but Connacht defended well with Darragh Murray executing an excellent lineout steal after Cardiff had gone to the right corner, while the Welsh were guilty of crossing after kicking to the left corner.
But Cardiff got back in the match when Ben Thomas bounced off Hugh Gavin in midfield to score, with the centre adding the conversion while Sheedy was receiving medical attention.
A superb break down the left by Harri Millard ended with Josh Adams scoring in the other corner but Thomas' conversion narrowly missed the target which left Connacht leading 21-20 with 19 minutes left.
Cardiff had a chance to hit the front but messed up another five-metre lineout and Connacht made them pay as Josh Ioane, Treacy and Hansen combined for Shayne Bolton to hold a lunge from Adams to score in the right corner. Crucially, Ionae added the conversion to put eight between them with 12 minutes left.
And Connacht wrapped up the issue three minutes from time when Paul Boyle barged over after Thomas was binned following a break by replacement scrum-half Caolin Blade.
Scorers: Connacht: Tries: Matthew Devine, Sean Jansen, Finn Treacy, Shayne Bolton, Paul Boyle. Cons: JJ Hanrahan (3), Josh Ioane (2).
Cardiff: Tries: Ray Lee-Lo, Ben Thomas, Josh Adams. Con: Thomas. Pen: Callum Sheedy.
Connacht: Mack Hansen; Shayne Bolton, Hugh Gavin, Bundee Aki, Finn Treacy; JJ Hanrahan, Matthew Devine; Jordan Duggan, Dave Heffernan (capt), Finlay Bealham; Oisín Dowling, Darragh Murray; Josh Murphy, Shamus Hurley-Langton, Sean Jansen
Replacements: Dylan Tierney-Martin (for Heffernan 44), Denis Buckley (for Duggan 56), Jack Aungier (for Bealham 57), Niall Murray (for Darragh Murray 66), Paul Boyle (for Hurley-Langton 52), Caolin Blade (for Devine 56), Josh Ioane (for Bolton 38-40, for Hanrahan 56), Cathal Forde (for Gavin 62)
Cardiff: Cameron Winnett; Josh Adams, Rey Lee-Lo, Ben Thomas, Harri Millard; Callum Sheedy, Johan Mulder; Danny Southworth, Liam Belcher (capt), Keiron Assiratti, Josh McNally, Teddy Williams, Alun Lawrence, James Botham, Taulupe Faletau
Replacements: Evan Lloyd (for Belcher 57), Corey Domachowski (for Southworth 57), Rhys Litterick (for Assiratti 53), Rory Thornton (for McNally 65), Alex Mann (for Faletau 52), Thomas Young (for Botham 65), Ellis Bevan (for Mulder 78), Rory Jennings (for Cheedy 60)
Referee: Luc Ramos (France)
