After the Frenchman had coolly sealed the near three-hour battle with the 23-year-old Australian 19th seed by punching down two aces, Pouille fell on his back and then sat looking stunned on his chair, soaking up the applause.
The 22-year-old had already bested his major performance by reaching the Wimbledon last 16 when downing Argentine Juan Martin del Potro as well as far surpassing his own expectations.
"Before the tournament, (it) was to win one match on grass. Yeah, now, of course, I'm very happy, very emotional with the win today," the 32nd seed told reporters.
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He and Tomic were two of the four players aged 23 and under in the fourth round -- the most at Wimbledon since 2010, when the youth wing included Britain's Andy Murray and now world number one Novak Djokovic.
The other of the four youngest players, Australia's Nick Krygios, was defeated in three sets by Murray on Centre Court.
"I had a big chance to make a semi at Wimbledon ... But I have to give credit to him, because he played the right tennis to win," said Tomic, who reached the Wimbledon quarter-finals in 2011 as a qualifier.
Next up for Pouille, who reached his tour-level final and broke into the top 50 this year, will be fellow 22-year-old Jiri Vesely or Tomas Berdych, who reached the final six years ago and has been a permanent fixture in the top 10 since July 2010.
"I think it will be one of my most important matches of my career so far. To reach the semi-final of a grand slam, of course, it's important," Pouille said.
"If it's Jiri Vesely, it's the same for him. If it's Berdych, he has already made the final here."
He will have to wait until Tuesday to see which man he will face as their all-Czech match was suspended in the fading light at 9:21 p.m. after Vesely took it to a fifth set shootout, winning a 71 minute fourth set on the tiebreak.
It was the only match in play and Berdych told the umpire it was "absolutely ridiculous" to still be on court as Vesely raced to a 6-1 lead. The 30-year-old got back to 8-8 before Vesely edged it, leaving the tie at 6-4 3-6 6-7(8) 7-6(9).
Berdych, who has been dogged by delays at this year's championships, then asked officials if the match could be moved to Centre Court to be finished off on Monday night, a request which was declined.
(Reporting by Alison Williams; Editing by Ken Ferris)
