Rhys Thomas' team-mates gave the prop the perfect get well message as two tries from wing Vili Iongi helped them to a hard-fought success.
Thomas is in a comfortable condition in hospital following heart surgery after being taken ill at training on Thursday.
Iongi's brace and a score from replacement prop Deacon Manu, plus three conversions and two penalties from Dan Newton secured a win that means a repeat performance at Sale next week will seal a last-four spot for the first time since 2006.
Irish, who were guilty of spurning a series of scoring chances, replied through four Tom Homer penalties and a converted try from Topsy Ojo that gave them the lead in the final quarter, but they could not hold off a strong Scarlets finish.
The Exiles showed positive intent from the off, spreading the play wide through the combined playmaking talents of Dan Bowden and Steve Shingler, playing against his former club for the first time just weeks since a furore erupted over his international eligibility.
The Premiership side could have grabbed an early try but Homer was adjudged to have knocked on as he attempted to ground an intelligent Jonathan Joseph grubber, but the full-back made amends by kicking a 12th minute penalty.
Newton replied in kind for the Scarlets before the Welsh side again came out on the right side of the video referee's decision as Tony Rowlands correctly ruled that wing Marland Yarde had failed to ground the ball after taking Bowden's inside pass.
And the Scarlets punished the Exiles profligacy by scoring the opening try against the run of play on the half-hour.
Centre Adam Warren straightened the line and fly-half Aled Thomas' floated pass allowed Newton to send Iongi sprinting over in the corner, with Newton adding a testing touchline conversion.
Irish lost Shingler to injury soon after, although his replacement Shontayne Hape was soon back on the bench as the visitors absorbed heavy pressure from a home side energised by their try.
Newton chipped behind the flat-footed Exiles defence and Hape, discarded by England for the Six Nations, committed a needless block that saw him head to the sin bin.
Newton could not land the resulting long-distance penalty, before the home side were given another let off when lock Bryn Evans and flanker David Sisi combined to ruin a two-man overlap during a frenetic finish to the opening half.
Two Homer penalties quickly trimmed the deficit to one point after the break and Yarde looked set to put the visitors back in front as he broke two tackles to race towards the post, only for Scarlets replacement Liam Davies to pull off a superb covering tackle and Irish to be penalised at the resulting ruck.
Irish frustrations briefly boiled over as scrum-half Darren Allinson landed a punch on Scarlets flanker Johnathan Edwards in the ensuing melee, but referee Nigel Owens let the Welshman off with a talking to.
The skirmish had a galvanising effect on the hosts, and they capitalised on some clumsy handling by Ojo to force a five-metre scrum, paving the way for replacement Deacon Manu to burrow over for a try confirmed by the video official and converted by Newton.
Homer quickly responded with his fourth penalty before Irish took back the lead when Ojo weaved through non-existent defence to cross behind the posts for a converted try.
But the lead lasted just six minutes as converted Scarlets pressure saw the Exiles penalised for not rolling away and Newton land the resulting penalty, before Iongi sealed the win by skating his way down the right flank in added time.
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