Just three of the eight T20 Blast matches due to take place today were able to play to a conclusion as a result of inclement weather conditions.
Ian Cockbain led the Gloucestershire charge with a half-century as they set their opponents a target of 138-7.
In reply, Sussex were dismissed for 125 inside 15 overs, with Jack Taylor finishing with bowling figures of 3-12.
Gary Wilson led the charge with a knock of 66 for Surrey as they set Essex a target of 166 for victory, but Ryan ten Doeschate, who finished 40 not out, hit the winning runs inside the final two overs to give the hosts the win.
Leicestershire Foxes were able to get their fixture against Northamptonshire underway, and were bowled out for 82, but the umpires called the match off before the visitors could begin their reply.
Results in full: Gloucestershire beat Sussex Sharks by 13 runs, Hampshire beat Kent Spitfires by 47 runs, Essex Eagles beat Surrey by five wickets
Abandoned: Glamorgan vs. Somerset, Leicestershire Foxes vs. Northamptonshire, Durham Jets vs. Nottinghamshire Outlaws, Birmingham Bears vs. Lancashire Lightning, Worcestershire Rapids vs. Yorkshire Vikings