It was a cautious start to the contest as both fighters waited on the back foot, sizing each other up.
It was Ren who edged the first round 3-2 and she managed to increase her advantage to three points after two.
Both combatants were still content to box at range and wait for an opening, which suited the Chinese fighter.
Esparza had cut the deficit to two points as they entered the final round, but struggled to get near Ren, who looked comfortable throughout the bout.
Ren kept the scores level in the decider and ran out a 10-8 winner.