The 35-year-old cueist lost to Jae Ho-cho from the Republic of Korea (RoK) in the semi-finals.
With the result, Chien has moved up one place in the world rankings to sixth place.
Turk Tayfun Tasdemir, 43, won the event and climbed to fifth place in the world rankings. Tasdemir defeated Cho, 38, in the final, but Cho has still climbed to third place in the rankings.
Earlier, Chien lost out to Martin Horn of Germany (world No 26) in the first match of the qualifying round in Group G. However, he enjoyed two consecutive victories over Choi Wan Young (No 79) and Heo Jung Han (No 11), both of the RoK, to progress to the quarter finals where he defeated Choi Sung Won of the RoK (17).
Another Vietnamese cueist Ngo Dinh Nai also rose two places from 16th to 14th after reaching the quarter-finals.
Although Nguyen Quoc Nguyen was ousted from the qualifying round, he still kept his No 9 place.
The first 2019 World Cup was held for the first time under a new format. The first day of the main draw after the pre-rounds was played in eight groups of four instead of direct knock-out. Two players per group, sixteen in total, moved up to the real knock-out stages on Saturday.
Chien, Nguyen and Nai will compete in the Survival Three-Cushion Masters in Incheon, the RoK, from February 28 to March 3.
