The visitors led 1-0 at half-time through the league’s second top goalscorer George Landais before Joe Shelley and Landais with his second netted in the second half.
The victory means Golds now need to win their final game of the season on Saturday against Newhaven to lift the Division 1 title for just the second time in their history.
Heath manager Steve Painter said: “We played quite well at times but the main difference was they took their chances. Even if Ollie (Moore) had scored you just felt they would still have gone on to win the game.
“They (Littlehampton) are the best team we’ve played all season, very strong going forward and in Joe Shelley they have the best player in the league, if they play as well next week at home to Newhaven then they will be champions.”
Heath started well as Mark Bevan struck a fierce shot from 30 yards to test the handling of Town’s keeper Jon Hendrick and Piers McDermott shot over the crossbar.
At the other end, Kieron Pamment intercepted a backpass from Dan Attwater but Eliott Flack was off his line quickly to deny an early goal. Minutes later, Attwater made amends for his mistake by clearing an effort off the line.
On 30 minutes, the visitors were awarded a corner and the ball was played into the Heath penalty area and gathered with ease by Flack, but the referee had spotted an off-the-ball incident resulting in a yellow card for Attwater and a penalty for Littlehampton which Landais gratefully accepted to give his team a narrow half-time lead.
Heath should have drawn level 10 minutes into the restart when Moore fired over from 12 yards.
Two minutes later, Heath were made to regret that miss when a counter-attack saw Liam Humphreys strike from distance parried by Flack and Shelley following up, slammed in the rebound.
Landais completed the scoring in the 62nd minute with a well executed shot from the edge of the penalty area.
Painter’s side now end their season away to Eastbourne United on Saturday.
Arundel have been deducted three points for fielding an ineligible player in their 2-1 win over Heath in January.
Alex Biggs should have been serving the second of a two-game suspension but Mullets said the suspension only showed up as one game on the Sussex FA governance website.
Heath will not be awarded the points.