Sam Warburton notched the sole try of the game for the Blues in the second half with London Irish only mustering five penalties - four from Adrian Jarvis and one from Delon Armitage.
Halfpenny's stellar performance with the boot comes a week after a wayward kicking performance in the 23-19 RaboDirect PRO12 defeat to leaders Leinster at the Cardiff City Stadium.
Despite that Cardiff kept their kicking faith in him for the trip to London Irish, and not Dan Parks, and Baber saluted Halfpenny for his ability to move on and this time put in a match-winning display.
"I thought it was vitally important Leigh was given the opportunity to put that to rest and he did just that. Our victory was down in no small part to his goal-kicking," said Baber.
"We seized the initiative after half-time, which is something we had talked about doing and it is another experience that will drive Leigh on into being an even better player."
Meanwhile Soane Tonga'uiha and England full-back Ben Foden both scored tries as Northampton overcame Cardiff's RaboDirect PRO12 rivals Scarlets 29-17 to boost their hopes of an Amlin Challenge Cup quarter-final.
Munster reached the Heineken Cup last eight with a 26-10 win over Castres while fellow Irish outfit Connacht fell 24-3 to Toulouse and Clermont punished Aironi 82-0.
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