Cory Allen scored an early well-constructed try for Blues, but a score from former Scarlets wing Andrew Fenby put Irish into a slender 16-13 half-time lead.
Home fly half Shane Geraghty charged down a kick from his opposite number to score and put Irish in control just minutes into the second half.
Wing Fenby grabbed a second try of the game before Gareth Anscombe’s late effort gave Blues some hope.
But it was the hosts that held firm to claim the points on offer and denied Blues any to take back to Wales as Irish went back top of Pool 1 with two games remaining in Europe.
Blues now face a home clash with Rovigo before they travel to Grenoble last up and know they now must better the results of Irish if they are to claim a quarter-final spot and potential home knockout game.
Alex Cuthbert claimed an early high ball before the returning Sam Warburton was straight into the action with a powerful run down the left wing.
Early scrum penalty against Blues saw Irish kick to the corner and a further penalty seconds later, for taking the lifter in the lineout, saw Tom Homer kick the home side into an early lead.
Slick hands from Blues put Macauley Cook free and into space down the middle and then Cory Allen popped up on the right wing as the visitors looked to play with continuity from the start.
Cuthbert then drove past men, as the forwards grouped behind him, before Blues went wide left with devastating impact on 11 minutes.
Gavin Evans, on his 100th
appearance, spotted the gap and intelligently popped a pass wide to Adam Thomas. The full back immediately stepped back in field and fed a pass out of a tackle to Allen who slid over. Anscombe added the difficult conversion from the touchline for a 7-3 lead.
The game was being played at real pace by both sides with Cuthbert rising highest to claim Anscombe’s high bomb in field before Richard Smith turned Irish with a drilled kick in behind.
Cuthbert was on fire as he blitzed past men before a kick in behind by Paulo caused panic. The resulting lineout went in field with Anscombe, Allen and Evans all going close before Irish turned over ball.
The home side cut the lead to a point with a penalty at the midpoint of the half after Blues were adjudged to have pulled down the jumper in the lineout.
A sustained period of pressure from Irish saw them pile on heat and win another penalty at the breakdown, with Homer slotting for a 9-7 lead to the home side.
The penalty count was stopping Blues build up a head of steam as they allowed Irish to kick clear and stop Hammett’s men gaining any territory and momentum.
Irish scored their first try of the game as Geraghty made a break in midfield and fed Ojo. The flying wing was pulled down short of the line by Allen, but with numbers out wide it was Fenby who dotted down for a 16-7 lead.
Anscombe hit back with two penalties as the hosts took a three-point lead into the dressing rooms at half-time.
Tempers flared at the breakdown at the start of the second half as both teams pushed for the ascendancy ahead of a big 40 minutes of European rugby.
Disaster struck for Blues as Anscombe saw his kick charged down and, in a repeat of the previous week, Geraghty was left with an unchallenged run under the posts. Homer added the conversion and at 23-13 it was all uphill task for Blues.
A scrum penalty saw Irish go further even ahead as Homer nudged the simple kick over from directly in front of the posts.
The visiting forwards looked to respond to the bright home start and won a penalty that was kicked to the corner. However, Irish held firm and then won a free kick at the resulting scrum.
Blues were having to work hard in defence to hold Irish out as Gethin Jenkins forced a turnover.
Josh Navidi looked to spark an attack as he rolled out of a tackle, but the whistle of referee Andrew McMenemy went against the visitors once more.
Hammer looked to shake Blues up as Lewis Jones, Kristian Dacey and Sam Hobbs were introduced just after the hour mark.
Anscombe slotted a penalty to cut the lead to 10 points before more heartbreak for Blues as, from the restart, the ball found Fenby who raced over. Blues appealed for a knock on in vain and the try was given for a 31-16 lead.
A further penalty from Homer left shell-shocked Blues needing a quick response, but they got just that as the ball was kept alive and Anscombe spotted a gap to race over and score his first try for the region to cut the lead back to 34-23.
Irish needed one more try to secure a try bonus point and with seven minutes left thought they had it but were held up as the forwards thumped their way over.
But Blues held firm and the game slowly ebbed away as Hammett’s men were forced to return back to Wales empty-handed and will look to bounce back in Round 5 against Rovigo in the New Year.
06m Homer p 3-0
11m Allen t Anscombe c 3-7
23m Homer p 6-7
28m Homer p 9-7
34m Fenby t Homer c 16-7
37m Anscombe p 16-10
39m Anscombe p 16-13
47m Geraghty t Homer c 23-13
53m Homer p 26-13
66m Anscombe p 26-16
67m Fenby t 31-16
68m Homer p 34-16
72m Anscombe t Anscombe c 34-23
Cardiff Blues: 15 Adam Thomas, 14 Alex Cuthbert, 13 Cory Allen, 12 Gavin Evans (Davies 68), 11 Richard Smith, 10 Gareth Anscombe, 9 Lloyd Williams (Jones 63), 1 Gethin Jenkins (Hobbs 65), 2 Matthew Rees (Dacey 63), 3 Adam Jones (Mitchell 50 (Jones 77)), 4 Filo Paulo, 5 Josh Turnbull, 6 Macauley Cook, 7 Sam Warburton (Jenkins 69), 8 Josh Navidi
Replacements: 16 Kristian Dacey, 17 Sam Hobbs, 18 Craig Mitchell, 19 Ellis Jenkins, 20 Manoa Vosawai, 21 Lewis Jones, 22 Gareth Davies, 23 Dan Fish