The Filipino tennis star overcame a late change of opponent to deliver a composed performance, completing the victory in one hour and 23 minutes.
Eala was originally scheduled to face American Alycia Parks in her opening match, but Parks withdrew shortly before the encounter because of an injury, giving 18-year-old lucky loser Jones an opportunity to enter the main draw.
Despite the unexpected switch, the second seed made an impressive start, racing into a 4-0 lead in the opening set.
Jones responded by winning three consecutive games to reduce the deficit, but Eala maintained her composure to close out the set 6-4.
The 21-year-old continued her strong performance in the second set, establishing a 5-1 advantage before Jones fought back to recover one break.
However, Eala held firm to seal the set 6-3 and secure her place in the last 16.
Speaking after the match, Eala admitted that the late opponent change was an unusual experience but stressed the importance of remaining prepared for unexpected situations on the professional tour.
The Filipina also expressed her affection for Hong Kong, describing the tournament as a familiar environment because of her previous appearances and the strong Filipino community in the city.
Eala sets up last-16 meeting with Valentova
The victory sends Eala into the second round, where she will face Czech teenager Tereza Valentova.
Valentova booked her place in the last 16 after defeating Japan's Himeno Sakatsume 6-3, 7-5.
Eala, who reached a career-high ranking of world number 17, will be hoping to continue her impressive campaign as she targets another significant achievement on the WTA Tour.
The second seed is also looking to build on a breakthrough season in which she became the first Filipina to win a WTA Tour singles title.