The German, a two-time champion at the season-ending tournament of the top eight players, bagged a break in each set to clinch a 6-4, 6-4 victory over the 20-year-old Spaniard, who has played a sensational first season on tour and has risen from the mid-100s to the top 10 in less than 12 months.
Jodar, however, could do little to tame Zverev's booming serve, and the most experienced ATP Finals player in the field, playing his 31st match, earned a break to go 4-3 up with a superb backhand down the line.
The Spaniard had two rare break chances at 5-4 behind but could not convert either. Instead, Zverev bagged the set in the next game and grabbed a break early in the second set to open up a 3-1 lead.
He was never troubled again as he comfortably held serve for his first win in the John McEnroe group.
World number four Ben Shelton takes on France's Arthur Fils in the other match of the group on Sunday.