This was a passionate cross-border clash that swung this way and that before settling on Swansea's second away win of the season.
Cheltenham began the game strongly and gave themselves the perfect start with a goal after only four minutes.
Goalkeeper Shane Higgs launched a long clearance down field that was flicked on by first Damian Spencer and then Paul Connor.
The ball travelled in behind full-back Angel Rangel and Cheltenham midfielder Ashley Vincent produced an electric burst of pace to nip in and roll a shot beyond Dorus de Vries from a 45 degree angle.
Swansea found it hard to get their passing game going in the early stages and Cheltenham had another good chance on the half-hour mark when a Lee Ridley cross was nodded down by Connor and Andy Lindegaard saw a thundering drive parried by de Vries.
The visitors finally built up some momentum in the minutes leading up to half-time and it was leading scorer Jason Scotland who almost levelled for them.
The Trinidad & Tobago international had a shot saved by Higgs then turned sharply on the edge of the box before brushing the crossbar with a firm shot.
Scotland finally achieved the breakthrough for his team five minutes after the re-start, although there was a whiff of controversy about it.
Right-back Rangel lifted a pass forward and the Cheltenham defence halted waiting for an offside flag against Scotland, who was running back towards the play.
No flag was forthcoming and Scotland ran forward to plant his sixth goal of the season beyond Higgs.
De Vries dived at full-length to save a shot from Connor, but the Swans got the crucial second goal on 69 minutes.
Andy Robinson took an in-swinging corner from the left that was headed clear by Michael Townsend.
Robinson picked up the loose ball and cut inside onto his right foot before driving a low shot past Higgs from the corner of the penalty area.
Cheltenham huffed and puffed after that but were unable to find a way past a Swansea side that had showed far more cohesion and attacking threat in the second half.