Jenkins replaces Bath loosehead Paul James, who is unavailable as the Wallabies clash falls outside the International Rugby Board's autumn Test window, with Andrews in for knee injury victim Aaron Jarvis.
Evans, meanwhile, takes over from Bradley Davies, who was left with severe concussion following a first-minute incident last weekend that resulted in All Blacks hooker Andrew Hore being cited and subsequently banned for five weeks.
The only form change is in the back-row, where Shingler takes over from former Wales captain Ryan Jones, who is on the bench. Wing George North remains sidelined due to a hip injury, while the Wales bench includes uncapped Scarlets prop Samson Lee, who celebrates his 20th birthday on Friday.
Wales have lost their last six Tests against all opponents - their worst run of defeats since the 2002-03 season - and they will drop outside the world's top eight teams if they come unstuck on Saturday.
A Wallabies victory would condemn Wales to the third tier of countries for next Monday's 2015 World Cup draw in London, while also meaning an autumn whitewash following the RBS 6 Nations champions' earlier defeats this month to Argentina, Samoa and New Zealand.
Gatland said: "We need to pick up again from where we left off in the second half last week. We managed to retain 73 per cent possession after the break against the All Blacks and win the territory battle, and we need to put Australia under similar pressure from the outset.
"We have played them regularly over the last couple of years and have come close to winning on a number of occasions, but have not quite been able to get ourselves over the chalk of the finish line.
"Both sides have had injuries to cope with, but there is every reason for optimism."
Wales team: L Halfpenny (Cardiff Blues); A Cuthbert (Cardiff Blues), J Davies (Scarlets), J Roberts (Cardiff Blues), L Williams (Scarlets); R Priestland (Scarlets), M Phillips (Bayonne); G Jenkins (Toulon), M Rees (Scarlets), S Andrews (Cardiff Blues), I Evans (Ospreys), L Charteris (Perpignan), A Shingler (Scarlets), S Warburton (Cardiff Blues, capt), T Faletau (Newport Gwent Dragons).
Replacements: K Owens (Scarlets), R Bevington (Ospreys), S Lee (Scarlets), R Jones (Ospreys), J Tipuric (Ospreys), T Knoyle (Scarlets), D Biggar (Ospreys), S Williams (Scarlets).