Gatland was forced to make one change after winger George North, arguably his side's best player last Saturday in Auckland, was ruled out of the series with a hamstring injury.
Liam Williams, who also impressed from fullback, has moved to the right wing in place of North, and Rhys Patchell takes the No 15 jersey.
Gatland played several of his fringe players against the Waikato Chiefs on Tuesday to give them a chance to push for test selection.
Although Wales were beaten 40-7 by the under-strength Super Rugby side, Luke Charteris, who captained the side, has been rewarded and will replace Bradley Davies in the second row.
Rhys Priestland comes onto the bench in place of New Zealand-born Gareth Anscombe, who was a late withdrawal from the Chiefs match with injury.
Wales were combative for about 60 minutes of the first test at Eden Park but were over-run by the All Blacks in the final quarter to lose 39-21.
Gatland said they needed to ensure that did not happen again at Wellington Regional Stadium.
"It is important we go out on Saturday with the confidence to play for 80 minutes in what will be another huge test match," he said in a statement.
Wales: 15-Rhys Patchell, 14-Liam Williams, 13-Jonathan Davies, 12-Jamie Roberts, 11-Hallam Amos, 10-Dan Biggar, 9-Rhys Webb, 8-Taulupe Faletau, 7-Sam Warburton (captain), 6-Ross Moriarty, 5-Alun Wyn Jones, 4-Luke Charteris, 3-Samson Lee, 2-Ken Owens, 1-Gethin Jenkins.
Replacements: 16-Scott Baldwin, 17-Rob Evans, 18-Tomas Francis, 19-Bradley Davies, 20-Ellis Jenkins, 21-Gareth Davies, 22-Rhys Priestland, 23-Scott Williams.
