Andhra Pradesh Circle scored a healthy 207/2 in 20 overs, while Odisha Circle could manage only 171/8 in their stipulated overs.
S Kranthi starred with the bat for AP, scoring a fluent 110 in just 66 balls.
In other matches: Gujarat beat Bihar, Jammu Kashmir beat Chhattisgarh, Assam beat Kerala, Delhi beat Himachal Pradesh and Tamil Nadu beat Maharashtra.
Earlier, Vice-Chancellor of Andhra University G S N Raju inaugurated the at Diamond Jubilee Outdoor Stadium.
Fourteen Postal Circles (States) are participating in the event whose final will be played on January 23.