England star Robinson, who featured at full-back in the first Test loss to the All Blacks, will be on the right wing, while back row forward Corry features at blindside flanker.
Test places are up for grabs as the Lions look to square the series in Wellington next Saturday.
Head coach Sir Clive Woodward, though, did not consider Stephen Jones, Dwayne Peel, Ben Kay or Gethin Jenkins because of minor knocks, while Gavin Henson misses out due to a slight groin strain.
Wales lock Brent Cockbain, tour replacement for the banned Danny Grewcock, earns an immediate chance off the bench.
Cockbain will link up with the Lions from Australia, rather than the UK, removing any prospect of jet lag.
Scottish hooker Gordon Bulloch will be captain for the second time on tour but among those hoping to impress Woodward will be full-back Geordan Murphy, wing Shane Williams, lock Donncha O'Callaghan and flanker Martyn Williams.
Woodward said: "Following Saturday's disappointing performance, this is a big opportunity to regain momentum and get everyone in the right frame of mind before the second Test, which I believe that we can win.
"Competition for test places is now intense. There are players involved in Tuesday's match who will also be involved in the Test.
"Obviously injuries, such as those to Brian O'Driscoll and Richard Hill, will force us to make some changes, but there will be changes beyond that."
Assistant coach Ian McGeechan added: "The players selected for the Manawatu game have a big responsibility now, to play good rugby and get us back to winning ways.
"That would give us a big lift as we move towards Saturday and a Test we have to win."
British and Irish Lions team to face Manawatu in Palmerston North.
Geordan Murphy (Leicester Tigers and Ireland); Jason Robinson (Sale Sharks and England), Ollie Smith (Leicester Tigers and England), Gordon D'Arcy (Leinster and Ireland), Shane Williams (Ospreys and Wales); Charlie Hodgson (Sale Sharks and England), Chris Cusiter (Borders and Scotland); Andy Sheridan (Sale Sharks and England), Gordon Bulloch (capt, Glasgow and Scotland), John Hayes (Munster and Ireland), Simon Shaw (London Wasps and England), Donncha O'Callaghan (Munster and Ireland), Martin Corry (Leicester Tigers and England), Martyn Williams (Blues and Wales), Michael Owen (Dragons and Wales).
Replacements: Andy Titterrell (Sale Sharks and England), Matt Stevens (Bath and England), Brent Cockbain (Ospreys and Wales), Neil Back (Leicester Tigers), Gareth Cooper (Dragons and Wales), Ronan O'Gara (Munster and Ireland), Mark Cueto (Sale Sharks and England).