The clubs go head-to-head again next weekend with the Welsh team holding a four-point advantage in the chase for quarter-final qualification.
Richard Smith set the Blues on track for a vital win, scoring one try and creating another as Blues maintained their unbeaten start in Europe and take top spot in their group.
Lloyd Williams and Kristian Dacey both scored in the second-half while Gareth Anscombe kicked nine points.
But London Irish claimed the first and last points of the game through Geoff Cross’ early score and a late penalty try to give them hope ahead of next week’s return tie.
Shane Geraghty missed his first chance but the Exiles profited when his opposite number Gareth Anscombe was charged down.
Scotland prop Cross blocked the kick and then benefitted from a kind bounce to score his first try for the club, unopposed under the posts. Geraghty converted for an early 7-0 lead after just eight minutes.
Anscombe and Cardiff hit back straight away through the fly-half’s clever chip.
Smith pounced and after opting to ignore two team-mates on his shoulder, he used his considerable strength to shrug off his tackler and score.
Anscombe converted for his first points in Europe but was twice wide of the mark before half-time.
Blues began the second half at real pace and the pressure told as Irish flanker Jebb Sinclair saw a yellow card after just five minutes.
But despite setting up camp inside the Exiles’ 22, Blues failed to capitalise on their advantage.
Evans and Macauley Cook went close before Anscombe kicked a penalty to give Blues the lead for the first time.
But they sensed a chance to hammer home their advantage and captain Rees repeatedly turned down further shots at goal in search of a try.
And they looked to have got it when Jenkins was at the tail of a thundering lineout drive. Blues players and fans celebrated but the video official ruled it was ‘inconclusive’ and the try was cancelled out.
Navidi was then stopped agonisingly short from the resulting scrum and Cuthbert then failed to collect from Williams. And when Sinclair returned, Blues looked to have blown their chance.
But once again the power of Smith proved telling as he bounced off two tackles to release Allen out wide. Allen looked to have held on too long but Williams picked up and darted over in the corner, from where Anscombe converted.
More forward pressure finally told when replacement hooker Dacey powered over from close range four minutes from time.
But Irish mustered a late response and after Sinclair’s try was ruled out by the video official, referee Ruiz, who contributed to an entertaining contest, awarded a penalty try after the Blues collapsed the scrum in the final play of the game.
