Lunch West Indies 283 & 258 for 7 (Brathwaite 110, Chanderpaul 45, Joseph 14*, Chase 13*, Lyon 4-81) need 240 more runs to beat Australia 598 for 4 dec and 182 for 2 dec
Extracting bounce and occasional sharp spin on a relatively sedate surface, Lyon continued his strong form at the Perth ground, having previously taken seven wickets combined in the fourth innings of victories over India and New Zealand.
His performance meant Cummins has not been required to bowl ahead of the day-night second Test starting on Thursday at Adelaide Oval. Like he did late on day four after starting the innings off the field, Cummins was on the field and appeared to be moving without obvious discomfort.
West Indies started the day on 192 for 3 and needing 306 runs for an unlikely victory with Brathwaite holding their hopes after batting through two sessions on the fourth day.
But the task, perhaps predictably, has proven difficult. Mayers, who did not bowl in Australia's second innings because of a strain in his right teres major muscle, had an early escape after surviving an lbw shout from Lyon. But replays later showed that he had inside-edged to silly point. Mayers capitalised on his good fortune by drilling a cover drive for four to push West Indies past 200.
Lyon had the last laugh, though, when Mayers edged a good-length delivery to first slip. It was Lyon's 443rd Test wicket, moving him past R Ashwin and into eight spot on the all-time Test wicket-taking list.
After batting aggressively late on day four, Brathwaite reverted to his usual defensive approach in an effort to blunt Australia's attack. Having effectively collared Lyon on day four, particularly countering the bounce with superb sweeps, Brathwaite finally counter-attacked with a boundary over long-on.
But Brathwaite's knock soon ended when he was bowled by Lyon, and West Indies' faint chances of survival might have gone him - he trudged off to a loud ovation from the smattering of fans who took advantage of the day's free entry.
Bar a miracle, it might just be a matter of time before Australia extend West Indies' Test drought in the country.