Both sides struggled to contend with the blustery conditions at Hayes Lane and it showed with Lucas Dawson's 36th-minute effort from 25 yards the best chance of the first half.
Bromley forward Tobi Sho-Silva saw an effort cleared off the line by Sam Hughes at the start of the second half as the game began to liven up.
Hughes then crossed for Evan Horwood but the Chester defender could only strike into the side-netting.
Bromley's best chance came when Louis Dennis was denied by a superb save from Alex Lynch, before Durrell's 25-yard effort on 88 minutes saw Chester end their three-game losing run and pick up only their third win of 2017.
Match report supplied by the Press Association.
Match ends, Bromley 0, Chester FC 1.
Second Half ends, Bromley 0, Chester FC 1.
Goal!  Bromley 0, Chester FC 1. Elliott Durrell (Chester FC).
Substitution, Chester FC. Wade Joyce replaces Sam Hughes.
Substitution, Bromley. Shane McLoughlin replaces Blair Turgott.
Substitution, Bromley. George Porter replaces Ryan Hall.
Substitution, Bromley. Connor Dymond replaces Lee Minshull.
Substitution, Chester FC. Blaine Hudson replaces Lucas Dawson.
Substitution, Chester FC. Evan Horwood replaces Johnny Hunt.
Second Half begins Bromley 0, Chester FC 0.
First Half ends, Bromley 0, Chester FC 0.
Blair Turgott (Bromley) is shown the yellow card.
Lee Minshull (Bromley) is shown the yellow card.
Tom Shaw (Chester FC) is shown the yellow card.
Lucas Dawson (Chester FC) is shown the yellow card.
First Half begins.
Lineups are announced and players are warming up.
Elliott Durrell's late winner helped Chester end their slump in the National League with victory at Bromley.