The home team never stopped running on the greasy pitch, and punished Cheltenham for some slack finishing.
Cheltenham started well in the heavy, driving rain and in the first minute they won two corners as Hartlepool keeper Arran Lee-Barrett pushed shots from Lloyd Owusu and Michael Townsend wide.
But the home team soon took command, jumping in front on 20 minutes when the Town defence failed to clear Jamie McCunnie's left-wing free-kick and James Brown ended a scramble deep in the box with a good close-range finish.
Now the Cheltenham defence had to cope with a lot of pressure as the ball skidded towards them almost non-stop, and five minutes after the first goal Joel Porter was wide from close range after Town keeper Shane Higgs parried a Brown shot.
Hartlepool were helped to a two-goal lead three minutes into the second half, Town defender Andy Gallinagh diverting Antony Sweeney's right-wing cross into his own net at the far post.
The third came for the home team on 62 minutes when Town keeper Shane Higgs made a mess of another Sweeney cross from the right and Andy Monkhouse slotted in easily from an angle on the left.
Just before that Gavin Caines' header hit the home bar, and later an effort from sub Paul Connor came back off the post as Town tried to fight back, but they were killed off in 87 minutes when home sub Michael Mackay latched on to a long ball from the back to score the fourth.
Owusu powered in a header from an 89th minute corner for Town's consolation, but it came far too late to make any difference.