A tight and closely fought first half saw the teams go in deadlocked at 7-7 after a charged down try from Irish front row Geoff Cross was cancelled out by a weaving solo effort from Smith.
The impressive home wide man fired Blues into life in the second half as he was the catalyst for the best move of the game that saw livewire scrum half Lloyd Williams dot down.
Prolific hooker Kristian Dacey was also once again among the tries as he touched down to settle any nerves.
The visitors did secure a late penalty try but left empty handed as Blues shot to the top of the standings and with destiny in their own hands ahead of the return clash at the Madejski Stadium next weekend.
A lively opening ten minutes saw wing Topsy Ojo collect an intercept and threaten an early score while centre Shane Geraghty could not reward an impressive opening spell from the visitors as he screwed a penalty wide left.
Both team were looking to adopt an expansive game plan, yet the game’s opening score came from a front row and from absolutely nowhere.
As Anscombe looked to clear, his kick was charged down by Cross who steadied himself and crashed over unopposed to stun the home faithful.
Anscombe’s response was emphatic. The next attack saw the fly half produce a peach of a kick in behind and Smith picked up at full pace, cut back inside his opposite man and powered through tackles to score.
The tackles were flying in as the returning Cory Allen unceremoniously dumped Alex Lewington out before the visiting wing had no choice but to again head for the tramlines as Anscombe perfectly kicked into wide open space.
The momentum, though, looked to shift at the mid-point of the half as home skipper Matthew Rees was sin binned by French referee Alexandre Ruiz after a series of breakdown penalties. Geraghty, though, pulled the resulting penalty wide left once more.
Anscombe also saw a kick drift across the posts, after a home penalty for a powerful driving maul.
The game was beginning to get stretched as both teams looked to play with tempo with the all-action Josh Navidi and back row partner Ellis Jenkins punching holes in the Irish defence.
A booming high up and under kick from Anscombe resulted in another penalty, with Geraghty the man caught accidentally offside, but the home fly half saw his kick fall left of the target from long range as the teams went into the dressing rooms level.
Blues turned up the heat at the start of the second half and Jebb Sinclair was the next to break the patience of the French officials at the breakdown, as he was sent for ten minutes in the sin bin.
Blues duly kicked deep for the corner and won a subsequent penalty for offside, after a searing burst from Macauley Cook, that Anscombe nudged over for a 10-7 lead.
Alex Cuthbert was into the action as he picked up Allen’s grubber kick through and when Craig Mitchell burst through tackles another penalty was secured. Anscombe this time went for the corner with Irish a man down and the tension cranked up.
The home pack rumbled over from the lineout and Gethin Jenkins looked to be the man on the spot to place it down. But, after consulting with the TMO, the try was not given to the bemusement of the home crowd.
More pressure saw Navidi made a sweeping break but he was held out and then another lineout was dragged down for a penalty as the visitors looked to hold firm.
Irish were working exceptionally hard to keep Blues at bay, but the move of the match just after the hour mark split them open in devastating fashion.
Cuthbert took the high ball and fed Thomas who found the elusive running Smith. The wing broke past two men and was away before he released Allen into space down the left. The Wales international was hauled down, but was alert enough to pop the pass to Williams who was in.
A penalty for not releasing gave Tom Homer his first kick of the game and chance to respond with ten minutes left, but he pushed his kick way wide right of the target.
A breakout from the hard-working Turnbull had the crowd on its feet in the closing stages before a brilliant break from Lewis Jones down then shortside saw him stay in touch and then cleverly win a lineout.
Blues once again drove with real desire and battered the line from the throw and, with a penalty already secured, it was hooker Dacey who smashed over from close range to a thunderous reception.
Irish looked to respond and did secure a last minute penalty try after a driving maul went to the floor. But it took little of the gloss off for Blues who now head to the Madejski knowing the outcome of Pool 1 and qualification for knock out cup rugby is firmly in their hands.
08m Cross t Geraghty c 0-7
11m Smith t Anscombe c 7-7
48m Anscombe p 10-7
64m L Williams t Anscombe c 17-7
76m Dacey t Anscombe c 24-7
80m Penalty t Geraghty c 24-14
Cardiff Blues: 15 Adam Thomas, 14 Alex Cuthbert, 13 Cory Allen, 12 Gavin Evans, 11 Richard Smith, 10 Gareth Anscombe, 9 Lloyd Williams (L Jones 72), 1 Gethin Jenkins (Hobbs 72), 2 Matthew Rees (Dacey 62), 3 Adam Jones (Mitchell 48), 4 Filo Paulo (Vosawai 74), 5 Josh Turnbull, 6 Macauley Cook, 7 Ellis Jenkins (Dacey 26-32, Watts-Jones 66), 8 Josh Navidi
Replacements: 16 Kristian Dacey, 17 Sam Hobbs, 18 Craig Mitchell, 19 Rory Watts-Jones, 20 Manoa Vosawai, 21 Lewis Jones, 22 Gareth Davies, 23 Dan Fish