Sunday's matches will see Peyper take charge of his 50th test (and his first quarter-final) with Wales versus France in Oita, while Barnes will round-off the weekend's action by refereeing hosts Japan against South Africa at Tokyo Stadium.
The All Blacks will face Ireland in perhaps the most intriguing matchup of the World Cup quarter-final stage.
Thanks to Japan's incredible 28-21 win over Scotland which saw the hosts top Pool A, All Blacks fans will be treated to a blockbuster matchup earlier than expected – a rematch of last year's Dublin clash where Ireland beat the All Blacks in convincing fashion.
During this tournament however, Ireland have been less convincing besides their first match against Scotland – losing to Japan, then failing to impress in their wins over Samoa and Russia.
The All Blacks, on the other hand, have been flying high since their win over the Springboks, but will be coming into the matchup cold after the cancellation of their final pool game against Italy.
Quarter-final draw
• England v Australia, Saturday, 8.15pm, Oita
• All Blacks v Ireland, Saturday, 11.15pm, Tokyo
• Wales v France, Sunday, 8.15pm, Oita
• Japan v South Africa, Sunday 11.15pm, Tokyo