First half goals were netted by Leigh Bremner (penalty) and Jack Clark after 31 and 38 minutes.
Recent lost games have seen Bury fall out of contention for a play-off promotion place, and the Suffolk side couldn't raise their game against a Cray side who were revitalised after their catastrophic 4-0 home defeat by Margate on Easter Monday. All the goals scored by fifth-placed Margate came after Cray's goalkeeper Andy Walker was injured in the 30th minute and defender Aaron Day had to take over in goal.
Cray recalled their former goalkeeper Steve Northwood for the trip to Bury and he kept a clean sheet to help the Wands get a much-needed win.
Cray: Northwood, Long, Clark, Saunders, Willy, Day (B Abbott 55), Fray, Stavrinou, Bremner (Pooley 73), Phillips, Power. Subs: Sackey, G Abbott, Jenkins.
Cray are at home to third-from-bottom Thurrock on Saturday (3pm).
An exhibition of Cray Wanderers FC history has opened at Bromley Central Library and will run from 3 to 17 April. This is in conjunction with London's annual CityRead event where the featured book this year is 'A Week in December' by Sebastian Faulks. Admission to the exhibition is free.