Kostyuk, the world No 27, proved far too strong as she crushed Eala 6-0, 6-1 in the opening round in Rome on Wednesday night.
The 22-year-old Ukrainian won the first 10 games of the match, lost just five points on serve and won and 60 of the 91 total points played.
Kostyuk is in fine form having reached the quarter-finals of the Madrid Open, where she lost a thrilling contest to world No 1 and eventual winner Aryna Sabalenka.
Eala was playing her maiden match at the Italian Open, and she is still in the very early stages of competing regularly on the WTA Tour.
The 19-year-old rising star made a sensational breakthrough in March as she reached the semi-finals of the Miami Open as a wildcard.
She stunned Jelena Ostapenko, Madison Keys and Iga Swiatek in straight sets at the Hard Rock Stadium before falling in a tough three-setter to Jessica Pegula.
The Filipina then reached the second round of the Challenger event in Oeiras before appearing at the Madrid Open, where she received a wildcard.
Eala defeated Viktoriya Tomova to set up a rematch with Swiatek in the second round in Madrid.
She gave the five-time Grand Slam winner another scare as she led by a set and a break before ultimately falling in three sets.
The 19-year-old entered the Italian Open main draw automatically after a number of withdrawals — the first time she did not have to qualify or receive a wildcard at a WTA 1000 tournament.
Despite her opening round exit in Rome, Eala is set to improve on the career-high ranking position of 70 she occupied heading into the event.
With the 10 points she has gained from losing in the first round, Eala has risen six places to a new projected best ranking of world No 64 in the Live WTA Rankings.
Eala is already the highest-ranked player from the Philippines in tennis history.
During the Italian Open, Eala told Tennis.com: “I didn’t expect such a big Filipino population here in Rome.
“But even just walking the streets, I’ve run into Filipinos five times already. When we walk in the streets, you know when you’re seeing another Filipino!
Eala is due to return to action next week as she is entered into the Parma Ladies Open, a WTA 125 tournament which runs during the second week of Rome from May 12-18.
The left-hander is then set to make her Grand Slam main draw debut at the French Open later this month.
