Cheltenham dominated the first half but were unable to create more than a handful of clear-cut chances. The best of these arrived after half an hour when an incredible shot from the half-way line by right-back Brian Wilson almost caught goalkeeper Boaz Myhill off his line. The American scrambled back to touch the ball over the crossbar and from the resulting corner, defender Jamie Victory rose highest to send a header inches wide.
Hull went close with a speculative effort from Stuart Green that cleared the crossbar and a header from Danny Allsopp that goalkeeper Shane Higgs needed to move sharply to collect.
If the first half had been controlled by the home side then it was a completely different story after the break as two goals in three minutes and a sending-off handed control to the visitors.
Allsopp claimed the first with a clinical finish after his striking partner Ben Burgess had flicked the ball into his path from a long clearance.
Two minutes later Cheltenham's Grant McCann smacked a free-kick from 30 yards straight into the defensive wall. Hull broke quickly up-field, leaving the Cheltenham defenders trailing and giving the chance for Burgess to score by lifting the ball over the goalkeeper from 10 yards.
Once the goal celebrations had died down there was more misery for the home team, who saw their lone striker Damian Spencer dismissed for an off the ball incident involving Hull defender Marc Joseph that had been spotted by one of the referee's assistants.
After that Hull did a successful job of keeping things under control to complete their 17th win of the season.
Hull manager Peter Taylor said: "Our first half performance was not good enough but we did well to get the first goal and that gave us the chance to go on and take the advantage.
"I'm disappointed that Spencer got sent off because we need him in Cheltenham's team causing problems for some of our promotion rivals."
His opposite number John Ward added: "Our defending was naieve for their two goals and my silly striker got himself sent off, which I cannot accept.
"But our effort and application was good and if we keep that up we will be okay."