In the last eight the Italian will play Ukraine's Marta Kostyuk, who beat American Ashlyn Krueger 6-4 6-4.
Eala's march to the fourth round, after her shock victory over defending champion Iga Swiatek and earlier defeat of Australia's Maya Joint, had captured the imagination of much of the 120 million population of the Philippines.
Sports arenas around the country hosted watch parties for thousands of supporters to cheer on the 21-year-old, who had broken new ground for her nation just by winning a match at the championships.
But the parties ultimately fell flat as it was 13th seed Paolini who triumphed 6-4 4-6 6-3.
Nerves were evident as Eala's first service game began with a double-fault, while another came courtesy of a serve so wide it hit the net post.
Paolini, a finalist in 2024, was a break up and serving for the set when Eala finally settled and landed her first blow.
But Paolini punished one too many 70mph Eala second serves to break again and take the opening set.
Breaks for both players came and went at the start of the second and it was Eala who came out on top, after shrugging off an awkward-looking slip on the baseline, to level the match.
A deciding set of bludgeoning baseline rallies swung Paolini's way when, at 3-4 down, Eala double-faulted again at precisely the wrong time.
One long forehand later and Paolini was serving for the match, which she secured after an enthralling two-hour, 21-minute contest.
If Kostyuk goes all the way the Centre Court crowd could see a backflip.
Kostyuk trained as a competitive gymnast for seven years when she was younger and celebrates big tournament wins with a backward somersault.
"I have some people, the volunteers, in the restaurant who are telling me 'can you do a backflip the next time you win a match?'," she said.
"I'm like 'guys, I save it for the only moment I win my first grand slam'. So hopefully."
Kostyuk is in her first Wimbledon quarter-final but has a 16-1 record on grass this season.