Darlington narrowly missed out on the end of season play-offs despite their victory as rivals Northampton Town also won to claim the last play-off position.
A big crowd gathered at the Williamson Motors Stadium, and Darlington were on the attack from the start of the game as they needed the goals to give themselves a chance.
In the opening minute an opportunity fell to striker Alun Armstrong, but he failed to control the ball and the early chance was lost.
The home side almost took the lead in the fourth minute when Clyde Wijnhard headed against the cross bar with Cheltenham keeper Shane Higgs well beaten.
Cheltenham had an early chance of their own in the sixth minute when a header from Damian Spencer went narrowly wide.
The visitors also went close in the 15th minute when Brian Wilson fired across the face of goal, and despite a lunge from Spencer he couldn't connect at the far post.
The visitors took the lead in the 29th minute when Russell failed to hold a 30-yard free-kick from Grant McCann and first to react to the loose ball was Spencer, who easily tapped in from close range.
Darlington brought on striker Akpo Sodje in the 33rd minute as he replaced the out-of-touch Armstrong.
The home side needed a goal before the interval and it came three minutes from the break when Wijnhard crossed from the right and a spectacular volley from Jonjo Dickman gave Higgs no chance.
With the crowd on their side Darlington took control of the second half, and Cheltenham battened down the hatch in preparation for the onslaught.
In the 48th minuten Neil Wainwright fired narrowly wide and then soon afterwards a shot from Curtis Fleming was blocked at the far post. Wainwright was involved again in the 62nd minute with a low drive that was easily dealt with by Higgs, and then the Cheltenham keeper was involved again when denying Wijnhard in the 68th minute.
Two minutes from time Wainwright put the home side in front with a header from close range, and then in the dying seconds a long ball from defence found Sodje who fired high into the net to complete the scoring.