Thompson shocked Rune, the seventh-seed world No.15, 4-6 7-6 (7-4) 6-3 while Hijikata was leading Tiafoe early in the third set when the American retired.
It was Hijikata's first tour win since defeating 478-ranked Bor Artnak in Acapulco in mid-April snapping six successive losses - though he had two matches in qualifying at Queens.
Rinky Hijikata gained his first tour-level win in two months after Frances Tiafoe retired. (AP PHOTO)
The result was also a fillip for Thompson who had lost his last five matches and not experienced victory since the opening round in Barcelona in mid-April.
It did looked as if his poor run would continue when Rune, a quarter-finalist at Wimbledon last year, took the opening set after it had been all square at 4-4.
But the resilient Thompson stepped up a gear to level the contest by taking a tight second set to a tiebreak where he put on a clinical display to force a decider.
The Australian, ranked 43rd in the world, then raced to a 3-0 lead and held firm to seal his third top-20 grasscourt win of his career.
While the British capital enjoyed a rare day of sunshine on Monday poor recent weather appeared to affect the courts and Rune kept slipping on the grass.
"This court is so slippy," the young Dane moaned to umpire James Keothavong.
Holger Rune was unhappy at court conditions at Queens, continually slipping and falling. (EPA PHOTO)
"Terrible court, what is this? I can't stand on the court. It's too wet. Call the supervisor. I fell three times. It's too wet. You think I'm falling on purpose?"
Thompson will next play record five-time Queen's champion Andy Murray or compatriot Alexei Popyrin, who came through qualifying. Their first round match is on Tuesday (Wednesday AEST) after Alex de Minaur kicks off the centre court action against Lorenzo Musetti.
Hijikata, who lost to Popyrin in s'Hertogenbosch last week, extended his stay at the west London event when Tiafoe retired. The American, who at No.28 is ranked 70 places higher, was forced to quit in the third set due to a right hip injury after he, too, fell.
The Sydneysider led 7-5 4-6 1-0 at the time.
Hijikata will face Ugo Humbert or Matteo Arnaldi next.
Earlier third seed Grigor Dimitrov rapidly dispatched Adrian Mannarino, 6-1 6-2, while struggling Brit Cameron Norrie later lost 7-6 (8-6) 3-6 7-6 (11-9) to big-serving Canadian Milos Raonic.
Now age 33 and ranked 186 after three years of injury issues Raonic remains a threat on grass and pounded down a series of 225kph serves hitting 47 aces in total, a record for a best-of-three sets ATP match.
"This small record, it's something special, something meaningful," he said. "I'm glad that behind that also stands a win because maybe I'd feel differently or maybe a bit more sour if I was to get that many free points and lose the match."
with agencies
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