Pakistan-born Anwar hammered a career-best 67 off 50 balls after Krishna Chandran (34), Khurram Khan (45) and Swapnil Patil (32) laid the foundation for a competitive total. Medium pacer Tendai Chatara (3/42) was the stand out bowler for Zimbabwe.
UAE, who are playing their first World Cup since 1996, achieved their highest ODI total by surpassing the 282 they made against Afghanistan last year.
Anwar, playing his eighth ODI, hit nine boundaries and reached his fifty with a straight six over the bowler's head.
Zimbabwe, opting to field at the scenic Saxton Oval, did not impress with the new ball the way they did in their fighting loss against South Africa.
The African team had reduced the opposition to 40 for two by the 11th over before the UAE middle-order rose to the occasion.
Amjad Javed (25*) and Mohammad Naveed (23*) provided the late burst with a 53-run stand off 41 balls for the eight wicket.