Vunipola was penalised four times and given a yellow card in the Lions' 24-21 victory in the second test in Wellington on Saturday as the visitors fell foul of referee Jerome Garces.
All Blacks first five-eighth Beauden Barrett slotted seven of 10 penalties to keep the world champions in the match despite being a man down after Sonny Bill Williams was sent off for a dangerous shoulder charge. He was later banned for four weeks.
Gatland spoke at length after the game about the need for greater discipline by the tourists as they seek to become the second Lions team to win a test series against the All Blacks.
"It is not very often on a Lions tour that you get to pick the same 23 for the following game," he said in a statement.
"We felt we should reward the players for the result and the courage that they showed in coming from behind from 18-9 down, digging themselves out of a hole and then finishing strongly in that last 10 to 15 minutes.
"There are some players who are pretty disappointed not to be selected and I understand that. It is what you would expect from competitive top athletes, they back themselves.
"But we have stressed all along that this is not all about the 23 players but about everyone in the squad - they have put their disappointment behind them and are helping the match-day squad prepare the best they can for the test match."
Meanwhile, Jordie Barrett and Ngani Laumape have been given their first starts for the All Blacks.
Julian Savea returns on the left wing and Israel Dagg, fullback last weekend, moves to the right wing.
Malakai Fekitoa, brought into the squad following Ryan Crotty's hamstring injury and Sonny Bill Williams' suspension, has been named on the reserves bench. Left wing Rieko Ioane, who has started the past two tests, has been left out of the 23, as has Waisake Naholo.
TEAMS
Lions: 15-Liam Williams, 14-Anthony Watson, 13-Jonathan Davies, 12-Owen Farrell, 11-Elliot Daly, 10-Jonathan Sexton, 9-Conor Murray, 8-Taulupe Faletau, 7-Sean O'Brien, 6-Sam Warburton (captain), 5-Alun Wyn Jones, 4-Maro Itoje, 3-Tadhg Furlong, 2-Jamie George, 1-Mako Vunipola.
Reserves: 16-Ken Owens, 17-Jack McGrath, 18-Kyle Sinckler, 19-Courtney Lawes, 20-CJ Stander, 21-Rhys Webb, 22-Ben Te'o, 23-Jack Nowell.
All Blacks: 15-Jordie Barrett, 14-Israel Dagg, 13-Anton Lienert-Brown, 12-Ngani Laumape, 11-Julian Savea, 10-Beauden Barrett, 9-Aaron Smith, 8-Kieran Read (captain), 7-Sam Cane, 6-Jerome Kaino, 5-Sam Whitelock, 4-Brodie Retallick, 3-Owen Franks, 2-Codie Taylor, 1-Joe Moody.
Reserves: 16-Nathan Harris, 17-Wyatt Crockett, 18-Charlie Faumuina, 19-Scott Barrett, 20-Ardie Savea, 21-TJ Perenara, 22-Aaron Cruden, 23-Malakai Fekitoa.