Simon Hamilton top scored with 79, while James Allan (33), skipper Matthew Parkins (42) and Brad Finch (43) all added crucial runs in Abbots’ total of 257-5.
In reply, OEs were all out for 233 in the 49th over, as Ravi Gokani took 3-46 and Parkins 3-33.
The win leaves Abbots in thirdspot in the table.