The tall seamer at one stage had the most expensive Test figures in England history, but the wickets of Cameron Green (45) and Steve Smith (61), both to poor shots, salvaged the visitors' day after a nightmare period for Carse.
It could have been three wickets in the over for Carse had Ben Duckett caught a sitter from Alex Carey's first ball in the gully off a brute of a short ball.
Australia went to stumps on Friday on 6-378, a lead of 44 and well on top, but England are still in it.
Carey, unbeaten on 46 from 45 balls, made England pay.
Will Jacks' one-handed screamer to dismiss Smith was an aberration in a poor final session in the field for the visitors on the second day.
Carse bowled mostly far too short and mixed that up with half-volleys to give Australia easy runs and a dream run towards a first-innings lead.
He had 1-95 off 12 overs and at that point, among bowlers who've sent down 10 overs in a Test innings, he had the most expensive England figures of all time, going at 7.92 per over.
Two wickets in his 13th over, while conceding just two runs, brought the 30-year-old back under Jack Leach's 1-102 at 7.84 runs per over in 2021 at the same venue.
Carse got better from there to finish with 3-113 off 17 overs, the seventh-most expensive figures ever for England.
The damage had been done. England failed to find a consistent line or length. Only six of the first 110 deliveries bowled would have hit the stumps.
Carse wasn't the only offender, but Mark Waugh, in Fox commentary, singled him out.
"He's bowled poorly, he has not put two balls in the one spot in any over," Waugh said.
"At this level, you've got to be better.
"The surface has just got enough in it and there's a little bit of up and down, so you don't have to try too much.
"You just have to bang that fullish length on that off-stump, but ... that's third-grade standard and all over the place.
"Sorry to those third-graders watching, but that is not great for a Test bowler."
To his credit, Carse fought back.
England captain Ben Stokes was forced to bowl his strike weapon Jofra Archer unchanged after the tea break because of the runs that were flowing.
Archer has bowled better, but he should have had Travis Head caught behind by Jamie Smith when he had made just three. Head fell on 33, but England's catching was poor, with Duckett also dropping Josh Inglis. Fortunately for England, that only cost them two runs.
Carse finished on a low note too, dropping a dolly at mid-off from luckless Archer to give Michael Neser a life.
England's first innings centurion Joe Root said the five dropped catches for the day, four under lights, were not for want of lack of preparation.
"We worked as hard as we could in the lead-up. We had five days of prep and did a lot of catching," Root said.
"We made sure the two days we had under lights we utilised well. Sometimes they don't stick.
"We know when we play our best cricket, and when we execute well, we are a very difficult side to play against."
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