The visitors won the toss and chose to bat, with a half-century from James Vince at the top of the batting order setting Hampshire up for a total of 177.
After a slow start to the home side's reply, Ed Joyce and Rory Hamilton-Brown had a 25-run partnership, but it was not enough to avoid the defeat.
Essex Eagles beat Glamorgan's total with just two balls to spare to make it two wins from two in the T20 Blast, leaving them at the top of the South Group.
A 96-run stand for the opening wicket from Jacques Rudolph and James Allenby appeared to have left Glamorgan in a strong position, but Essex's middle order were in dominant form to pass their 190-run target in the final over.
Worcestershire Rapids cruised to a 24-run win over Nottinghamshire Outlaws to seal their first win of the season and move up to fifth in the North Group.
Results in full: Gloucestershire beat Middlesex by five wickets, Kent beat Somerset by 42 runs, Hampshire beat Sussex by 18 runs, Essex beat Glamorgan with four wickets, Worcestershire beat Nottinghamshire by 24 runs, Northamptonshire beat Leicestershire by two wickets, Lancashire beat Derbyshire by 20 runs, Warwickshire against Yorkshire abandoned