Nevill, who was dropped on two, soaked up 153 deliveries and almost four hours in an unbeaten knock of 60.
But Nevill and the tail were left with far too much work to do as Australia were bowled out for 361, having resumed at 4-169 on Monday.
Proteas paceman Kagiso Rabada was inspirational in the absence of Steyn, swinging the ball both ways at pace to grab five wickets and be named man of the match.
The result follows Australia's shambolic 3-0 series loss in Sri Lanka earlier this year.
Australia haven't lost four Tests in a row since their calamitous tour of India in 2013. That debacle delivered a reminder of their subcontinent struggles, exposed bitter divides in the squad and essentially cost coach Mickey Arthur his job.
In Perth, Steve Smith spoke pre-match of a return to familiar surrounds and the resultant spike in confidence. Smith declared his batting order wouldn't be as brittle at home.
Smith was out for a duck in a first-innings collapse of 10-86 that changed the course of the game and left underdone pacemen Mitchell Starc and Peter Siddle bowling on four consecutive days.
Prior to the Indian whitewash Australia's most recent four-Test losing streak came in 1984. Again a dominant West Indies outfit were responsible but it still ended in tears for captain Kim Hughes, who offered an emotional resignation during the Test series in Australia.
There is no suggestion that Smith and coach Darren Lehmann will suffer the same fate as Hughes and Arthur. But a summer filled with losses similar to the first Test will put them under immense pressure.
It is Cricket Australia (CA) and national selectors who will cop the brunt of scrutiny before the second Test starts in Hobart on Saturday.
Joe Burns and Callum Ferguson will join the squad with Shaun Marsh ruled out of the fixture with a broken finger.
A debut for fast bowler Joe Mennie is the only other potential change to the XI with selectors already locking in their squad before the completion of the first Test.
Mitch Marsh, out for 26 on Monday following a first-innings duck, headlines the list of players who face the axe if they don't deliver at Bellerive.
AUSTRALIA HADN'T LOST THE FIRST TEST OF A HOME SUMMER SINCE 1988. WHAT HAS HAPPENED BETWEEN THOSE DEFEATS?
• Steve Smith, Mitchell Starc, Josh Hazlewood and Mitch Marsh have been born • Over 100 players have donned the baggy green
• The Australian Cricketers' Association has been formed and Twenty20 cricket has been created. Salaries have skyrocketed to a point where cricketers regularly feature in the BRW's annual Top 50 Sports Earners list
• Allan Border, Mark Taylor, Steve Waugh, Adam Gilchrist, Ricky Ponting, Michael Clarke, Shane Watson and Smith have served as Test skipper
• Bob Hawke, Paul Keating, John Howard, Kevin Rudd, Julia Gillard, Rudd, Tony Abbott and Malcom Turnbull have served as Prime Minister
• The internet has become publicly available and entered more than 85 per cent of Australian households
• Apartheid has ended. South Africa's cricket side have started touring again and won three Tests at the WACA.
