Brown: He feels good after fine win
United took the lead after 20 minutes with top scorer James Brown finishing well from close range after Town struggled to clear Jamie McCunnie's left-wing free-kick.
It was 2-0 to Pools three minutes after the break as Andy Gallinagh diverted Antony Sweeney's right-wing cross into his own net as it skidded in front of him at the far post.
The third came on 62 minutes when Robins keeper Shane Higgs pushed out another Sweeney cross, and Andy Monkhouse finished well from the left.
And the fourth followed three minutes from time when substitute Michael Mackay got on the end of a long ball down the right by McCunnie and finished well from a tight angle.
Lloyd Owusu headed in powerfully from an 89th-minute corner to give Town their consolation.