Darlington had to dig deep to register their sixth win in their last eight games as Cheltenham, who had lost only one game in their last 11, came close to grabbing an equaliser towards the end.
The home side began the game like an express train and Town keeper Shane Higgs pulled off two fine saves in the opening five minutes to deny Barry Conlon and David McGurk.
Cheltenham went close in the eighth minute when John Finnigan fired into the side netting from 10 yards out and soon afterwards McGurk fired the home side into the lead.
A Craig Russell corner was headed goalwards by Darlington captain Craig Liddle and McGurk helped the ball over the goalline via his knee in the 14th minute.
Conlon then had a shot saved by Higgs in the 17th minute as the home side dominated.
Russell was off target in the 26th minute with a shot from inside the area and then in a rare Town attack Liddle headed a deep cross from Tony Griffin from under his won crossbar.
Darlington doubled their advantage in the 38th minute thanks to Conlon who charged his way through the Cheltenham defence before smashing the ball past Higgs from close range to notch his 11th goal of the season.
The Darlington defence went missing seconds before the break and they paid for their lapse in concentration when Cheltenham striker Damian Spencer set up midfielder Grant McCann who fired into the bottom corner of the net to reduce the arrears.
In the second period Liddle went close with a 35 yard drive and then Conlon shot narrowly over the crossbar.
But the visitors ended the game strongly and Finnigan had a goal bound shot deflected away in the 73rd minute and then two minutes from time Spencer fired narrowly wide from inside the area.
Darlington manager David Hodgson said afterwards: "Tonight was a hard game but we came through it and deserved to win.
"I was disappointed with the crowd of less than 4,000. We need 6,000 otherwise there won't be a club to support." Cheltenham manager John Ward was disappointed with his sides first half showing and he said later: "We go to Doncaster at the weekend and need to play for 90 minutes not just the 45 that we did tonight."