England, trailing 2-0 in the series, bagged Australia's last four wickets for 59 to bowl them out for 385 and then, as temperatures continued to rise above 100 degrees Fahrenheit under a punishing sun, captain Alastair Cook (72) led from the front in a stumps total of 180 for four.
Cook and Carberry (43) put on an opening stand of 85 - the highest by either team so far in this series.
Carberry told Sky Sports 2: "I thought we played pretty well through some tough spots and it's nice to obviously get a decent platform up front for probably the first time in this series.
"I thought (captain Alastair Cook) Cookie played really, really well. It's nice to see him getting back to what we know he can do.
"He's had a lot on his plate the last few games and he's a really determined guy.
"He's scrapped hard today. I've seen him play more fluently but, in the in the context of the game, it was just what we needed - someone to dig in and keep the Aussies at bay."
Carberry paid the price for a misjudgment against Ryan Harris. A switch to round the wicket disorientated the left-hander sufficiently for a fatal hesitation over whether to leave or not, and, as he tried to take his bat out of the way, an involuntary edge cannoned back into the stumps.
But Carberry is relishing the challenge of his first Ashes series.
He added: "I really enjoyed it. I've never played at Perth before, so it's all an adventure for me I guess.
"I've really enjoyed batting in Australia in general.
"It's tough up front and then, once you get through that new ball period, it can be quite nice. A nice place to bat and the ball came on beautifully to the bat."
Carberry admitted England have been working on a different approach on the wicket in Perth due to the extra bounce.
He added: "It's something we've discussed in various team talks about being decisive and making sure if you're going for certain shots that you commit to them or similarly when you're leaving them - which I didn't do too well."
Ian Botham voiced his concern over the approach of the England batsmen. He felt they had overreacted to the criticism aimed at them for rash shot selection in the opening two Test defeats and had retreated too much into their shells.
He said: "It has gone from the sublime to the ridiculous. Everyone criticised their hooks and pulls in the first two Tests. Now I think they have gone totally the other way. It is like we have lost the knack of knocking it into holes and rotating the strike."
Australia bowling coach Craig McDermott was pleased with his attack in the latter part of the day, and said: "We started a bit rough with the ball, I suppose not as full as I'd like and not the lines that I'd like to see our guys bowling.
"But we got our act together after the break and the last sort of three to three-and-a-half hours we played really, really well and those two crucial wickets in the last session was a great end to the day for us."
McDermott reserved praise for Shane Watson and Nathan Lyon on the second day, but is pleased with the squad on the whole in regard to taking wickets.
He added: "Watto (Watson) is back to his best now and Nathan Lyon picked up Cook this afternoon with a bit of bounce with a cut shot - which is the second time now that's happened now in the series.
"Everyone keeps chiming in with good wickets for us and it's just a really good all-round attack from my point of view."
Mitchell Johnson, who made his mark in the first two Tests of this series, has not taken a wicket for 38 overs now, but McDermott admitted he was not worried.
He laughed: "Maybe he's got four up his sleeve for tomorrow.
"As an ex-tailender I wouldn't be too keen on facing him either so tomorrow morning we've got to bowl well, start well as we finished today with the old ball and hopefully get a wicket in that first 12 overs and then get stuck into the English with the new ball."