At close of play on a day shortened by a dramatic thunderstorm England were 299 for 4 - 186 runs adrift - with Butcher having gone for 116 and Graham Thorpe unbeaten on 70.
Resuming 432 runs adrift on 53 for 1 with Mike Atherton, their most dependable batsman, already back in the dressing room, England looked set to face a long and fractious day attempting to thwart Australia's efforts to enforce the follow-on and take an early lead in the five-Test series.
But Butcher defied expectations by firstly taking on the attack in a flourishing partnership with Nasser Hussain before adopting a more defensive game when the captain, Alec Stewart, threw away his wicket to leave England in a vulnerable position.
Butcher's discipline and composure ridiculed pre-Test predictions that he may struggle after scoring just nine runs in five first-class innings since being hit on the head batting on Perth's bouncy pitch three weeks ago.
During his century on Saturday, he needed painkillers to relieve a bad back after twisting badly during a run.
Instead, the Surrey man helped the tourists advance to a comfortable position when rain, bad light and lightning intervened and ended play 14.4 overs prematurely.
"The only way to go is believe in yourself, stay strong and believe you are going to get a run again sometime," he said. "I've tried to put it out of my mind to an extent, but there's always a time when doubts creep in.
"There's no one thing that I was doing wrong really and I hadn't batted long enough to work out what was wrong - it's hard working it out when you're gone in the first over.
"I've been helped by the other members of the tour squad because everyone wants everyone else to do well - it's not an act. In that type of environment, as long as you believe in yourself you will come out the other side."
Derek Pringle, page 21Reuse content