Ireland's hopes of a Grand Slam ended in Cardiff
Ireland forced a penalty try with Wales pulling down a maul.
Sexton converted and Ireland trailed by only four points with 10 minutes to play, setting up a grandstand finish in which Halfpenny landed his fifth penalty.
Jonathan Davies was sin-binned for a deliberate knock-on as Wales somehow held firm.
Wales captain Sam Warburton said: “That’s probably one of the most exhausted I’ve felt after a Test match. It was an unbelievable effort.”
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