Thompson was hoping to reach the third round at his home slam for the first time in 13 attempts.
Instead, the 31-year-old lost five straight games to give up a 4-1 lead in the fourth set to sink to a 6-7 (9-11) 6-3 6-2 6-4 defeat against Portugal's Nuno Borges.
Thompson has reached at least the last 32 at all three other slams and only last year he made the second week at Wimbledon, but he has puzzlingly only won five matches in 14 years at the Open.
He was quickly joined in the exit queue by compatriot Ajla Tomljanovic, who fell to Romanian Elena-Gabriela Ruse 6-4 6-4.
Later on Rod Laver Arena, wildcard Priscilla Hon had no answer to American teen Iva Jovic, going down 6-1 6-2 with the match finishing after midnight.
Talia Gibson was an early casualty on Wednesday but stood by her ultra-aggressive approach, despite letting slip a golden opportunity to advance to the third round of a grand slam for the first time.
Gibson had three match points in the 10th game of the second set of her second-round encounter with Diana Shnaider but failed to convert any of them, with the Russian counter-puncher grabbing the lifeline and going on to win 3-6 7-5 6-3.
That was despite the free-swinging West Australian dominating the outright winners count 39-24.
But a more telling statistic was the 49 unforced errors committed by Gibson, compared to just 25 from the more composed and match-hardened 23rd seed.
"It's obviously a bit disappointing to not get the win after having the match points there in the second set, but overall I'm going to be nothing but proud of myself," said the 21-year-old wildcard Gibson.
"I've done something that I haven't done before, put myself in a position to win the match and get through to the third round of a slam.
"So overall it was very exciting to see what my level can do."
Gibson had started the tournament strongly with victory over another Russian, Anna Blinkova.
The Australian was in the box seat to advance to the third round of a major for the first time when she had three match points at 5-4 in the second set.
"That's my game," Gibson said.
"I'm an aggressive player and, sure, more often than not I'm going to have a few more unforced errors than my opponent today, who doesn't have as aggressive a game as me.
"But there were still a lot of winners, and with an aggressive game that's something you're going to see."
While Gibson was left to rue a golden chance gone begging, countrywoman Storm Hunter was clearly outclassed in her second-round clash with Hailey Baptiste.
Hunter is on the comeback trail after recovering from a ruptured Achilles tendon.
The 31-year-old had done very well to advance through qualifying, before sending Spaniard Jessica Bouzas Maneiro on her way in the opening round.
But Baptiste presented a much stiffer challenge, with the powerhouse American winning 6-2 6-1 in a match that lasted little more than an hour.
The total of 11 Australians to have advanced to round two in Melbourne is the equal highest this century, but so far only Alex de Minaur, a 6-7 (5-7) 6-2 6-2 6-1 victor over Serb Hamad Medjedovic, is the only one to have made it into the third round.