Daniel Evans' individual try highlighted the Scarlets' attack, with winger Lee Williams also touching down.
eight Chris Hala'ufia, who supplied fellow back row Danaher the scoring pass with only six minutes on the clock.
Irish narrowly denied Scarlets the chance to take the lead early in the second half but the momentum had evidently shifted and when Jones added his third penalty the Welsh side were clearly in the driving seat.
The Exiles looked dangerous when Seilala Mapusua's try marked the first attack of the match, with the centre making a bulldozing run through midfield.
But with just over a minute left on the clock, substitute Peter Richards conceded a penalty in front of the posts and Wales fly half Jones landed the crucial kick to seal the win for the visitors.
The Exiles dealt what could have been a deadly blow in the 66th minute when an Evans pass intended for Mark Jones was intercepted by Tagicakibau, who had planted himself in the Llanelli line.
The sides entered half time on an even footing at 18 18 after Homer was shown a yellow card for taking Williams out in the air and Jones slotted a penalty.
London Irish v Scarlets
A pattern emerged as Scarlets responded two minutes later when Williams broke clear of a congested left wing and uncovered Hewat's lack of pace with a crafty chip that he got fingertips to in the Prada Envelope Wallet Price
Mapusua broke two tackles and the ball was recycled to number Prada Cosmetic Bag
Although Declan Danaher and Elvis Seveali'i also crossed to edge the try count three to two for Irish, the Madejski Stadium clash could have gone either way.
Jones demonstrated impressive form, finishing with 17 points after kicking outstandingly throughout and remained composed to help keep Scarlets at the top of Pool Six.
With only 15 minutes to go, Irish were trailing 21 18 and appeared to be out of chances until prolific Samoan winger Sailosi Tagicakibau ran in his seventh try of the season and put the Exiles in clear sight of victory.
Jones' conversion and a penalty helped to even the score, but once again Irish widened the gap when Mapusua used his boot to chip through to compatriot Seveali'i, who touched down.
Gradually, however, Irish crept back into contention and were inches short of crossing through Tagicakibau following a superb pass by Lamb.
ComfortableIrish appeared the comfortable leaders when Lamb secured Prada Robot Bag a drop goal shortly after, but Evans hit back for Scarlets by chipping over the Exiles' Prada Sunglasses Gold
The Samoan faced a 75 metre race to the line, but broke clear leaving no player able to stop him as he crossed beneath the posts, with Lamb converting.
advancing line, gathering and racing around Hewat before prevailing in the 25 metre pursuit to the line.
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