Bailo Camara had the first clear cut chance of the match, but could only drag his effort wide from 18 yards.
With 14 minutes played, Greenfield crossed behind the United defence to leave Ben Gray with a simple finish past Russ Tanner.
Littlehampton 'keeper Jon Hendrick was nearly embarrassed ten minutes later as his weak clearance was returned goalwards by Wes Tate, but Hendrick managed to claw Tate's 40 yard effort away for a corner.
From the corner, United came even closer to an equaliser when Acer Wake rattled the crossbar.
Littlehampton's second goal came five minutes into the second half as Gray turned provider when his cross evaded the outstretched Wake and found Greenfield who slotted by Tanner.
Tanner had to be alert to make three saves from close range to deny Littlehampton from extending their lead before United pulled a goal back.
Camara's corner was cleared to Tate, who from all of 35 yards, hit a half volley that sailed into the top corner of the net, leaving Hendrick motionless.
Hendrick denied Aaron Capon an equaliser following a header from the United man, but a counter attack after the resulting corner sealed the win as Shay Wiggins rifled home to condemn United to their second league defeat of the season.