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With the series lost after losing the first two Tests, and faced with eight players out with injury, coach Clive Woodward has dug deep into his squad to produce a new-look backline in a final effort to win one Test on tour.
Two of the four back line changes are the result of injuries to Jonny Wilkinson and Gavin Henson while Jason Robinson and Shane Williams have been dropped.
"It was a tough call on Robinson and Williams, but with the Test series standing at 2-0 it was right to give players that have performed well on the tour a chance to show what they can do," said Woodward.
"Cueto has had a really good trip and deserves his chance. If the series stood at 1-1 I'm not sure what I would have done, but at 2-0 both he and Murphy deserved to start.
"Geordan has had a good tour and to be honest he was unlucky not to be included in the first two Tests."
Cueto and Murphy both forced their way into the side after playing in the 17-13 win over Auckland on Tuesday, with Cueto doing enough to edge out Shane Horgan, who Woodward said was his initial prospect on the wing.
Murphy comes into the side for Williams and Josh Lewsey moves to the left wing.
The two other changes made by Woodward to the team that was heavily beaten by the All Blacks 18-48 in the second Test see Stephen Jones and Will Greenwood replace the injured Wilkinson and Henson.
Greenwood is listed as No 13, the outside centre position, but the Lions management have clarified he will play at inside centre while wearing No 13 for superstitious reasons.
Captain Gareth Thomas will start at outside centre wearing No 12.
Woodward, who delayed naming his team for 24 hours because of the high injury count in the squad, named an unchanged forward pack after prop Gethin Jenkins was cleared to play after being a doubt with an ankle injury.
On the bench, Irish flyhalf Ronan O'Gara is the only other new face in the Test 22, by virtue of being the only other fit outside half left in the squad.
For Murphy, it will be an extra special occasion playing a Test in Auckland where he spent several months as a schoolboy at Auckland Grammar alongside All Black reserve Doug Howlett.
And he believes the fact the score is 2-0 could give the Lions the glimmer of hope they need to snatch a win.
"To a certain extent we have nothing to lose and hopefully we can go out there with a real purpose and win the final match."
British and Irish Lions (15-1)
Geordan Murphy (IRL), Mark Cueto (ENG), Will Greenwood (ENG), Gareth Thomas (WAL) captain, Josh Lewsey (ENG) Stephen Jones (WAL), Dwayne Peel (WAL), Ryan Jones (WAL), Lewis Moody (ENG), Simon Easterby (IRL), Paul O'Connell (IRL), Donncha O'Callaghan (IRL), Julian White (ENG), Steve Thompson (ENG), Gethin Jenkins (WAL)
Reserves: Shane Byrne (IRL), Graham Rowntree (ENG), Martin Corry (ENG), Martyn Williams (WAL), Matt Dawson (ENG), Ronan O'Gara (IRL), Shane Horgan (IRL).
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