The two will lock horns when Leinster welcome Munster to the Aviva Stadium this weekend with Sexton desperate improve on a World Cup record that saw him miss seven on his 11 kicks at goal in the opening two matches.
Since then however, he has returned to RaboDirect PRO12 action and looked his old self against 36-28 win over Edinburgh, nailing seven out of nine kicks in difficult conditions.
And Murphy is tipping Sexton to come out on top in his battle with O'Gara in Dublin.
"Obviously, he didn't have the World Cup he wanted, but there was no sign of that since he came back," said Murphy.
"He's been fantastic. Possibly, there was a little bit of doubt in his mind over there. I don't think his confidence has taken a dent though.
"Since he's come back he's been working hard, but no harder than he would have had he been at 100 per cent over there. He's fine and I have no doubt he will bring it on against Munster."
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