Any Irish hopes of bouncing back from their opening weekend defeat to Edinburgh seemed to vanish when centre Shingler disappeared down the tunnel in the opening quarter.
But a disjointed Blues performance allowed the visitors to stay in touch, and Homer's booming boot punished their second-half indiscipline.
It all looked so promising for the Blues, full of confidence since their away win in Paris on the opening weekend, as they secured immediate control by capitalising on Irish's lack of urgency in the breakdown.
Parks' opening penalty was soon followed by Thomas' try as the home side showed their attacking intent by going for touch from a penalty instead of aiming for the posts.
Captain Paul Tito provided the perfect platform for the score as he won clean lineout ball and the visitors had no answer to the Blues' driving maul. Parks converted.
A comfortable evening for the home side looked on the cards as Shingler was sent off for a spear tackle on opposite number Dafydd Hewitt.
Before the match, Shingler had spoken of his desire to force his way into the Wales squad, but his dangerous tackle gave him little opportunity to impress coach Warren Gatland as he watched from the stand.
Irish enjoyed their best spell of the match as Homer landed nine penalty points in 13 minutes, bringing his side to within four points.
Homer was successful with five of his six attempts at goal
But the half took a whole different complexion in the final minute when Williams' blistering pace delivered the second Blues try.
Michael Paterson played a significant role as he won possession from Parks' kick-off, and scrum-half Williams caught the Irish defence napping as he burst clear from a ruck to score in the left corner.
The Blues started the second half with ominous intent, but Irish withstood the pressure, conceding just three points to a Parks penalty, and gradually began to enjoy dominance in the scrums.
Indiscipline crept into the home side's play, and full-back Homer capitalised in full with superb long-rang penalties to close the gap to 21-15 with 10 minutes remaining.
A fourth Parks penalty restored a nine-point Blues advantage, but Homer was again on hand to land his fifth kick to set up a tense finale.
With the losing bonus point already secured, the visitors spurned the opportunity to add another three points by setting up an attacking platform deep in the home side's 22.
The Blues looked in genuine danger as the Irish forwards gained valuable yards, but they failed to secure clean possession at a ruck, allowing a Blues boot to clear.
London Irish coach Toby Booth on Steven Shingler's red card:
"The way the game is being officiated around the tackle means if you are not precise you may pay a heavy price.
"The young lad is devastated. There was no malice in it. He is a young man coming back to Wales, wanting to impress. The guy jumped up and if you are not quite in control of your emotions or are just a little bit off with your timing, that is the outcome.
"The safety of players is paramount. These are big physical people playing a very tough game. But if you are out by a fine margin you can pay a heavy price and we have seen that."
Cardiff Blues caretaker coach Justin Burnell:
"When we arrived today, if someone had said it would not be a great performance but you will win I would have taken that.
"At the start we were very comfortable and had a good intensity like we had in Paris last week. We knew they would try to run and attack us.
"But in the second half, playing a man down, they kicked everything, threw numbers into the breakdown and slowed our ball down.
"Having said that, I am more than happy with the win."
Czekaj; Cuthbert, Laulala, Hewitt, James; Parks, L. Williams; G. Jenkins, T. Thomas, Filise, B. Davies, Tito, Paterson, Warburton, Rush.
Andrews for Laulala (59), Rees for L. Williams (59), Breeze for T. Thomas (71), Molitika for Rush (21).
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