The American ranked 102 powered past the second seed 6-3, 6-0 for the first title of her career and did not drop a set all week.
Despite being the underdog, the 26-year-old broke in the eighth game of the first set for a 5-3 lead at Victoria Park.
The American squandered the first set point but gobbled up the second to leave the large number of Eala fans in the arena stunned.
Eala, 21, who needed medical treatment and had a large bandage on her right knee, was immediately under pressure on her own serve at the start of the second set.
Liu eventually broke after an attritional opening game to grab the lead and, with that, Eala's resistance was broken.
Eala, at a career-high 17 in the world, had been seeking to win another title to go with the one she clinched in Washington, DC, in August.
That victory made her the first player from the Philippines to win a tournament on the WTA Tour.