So in the end a draw was just about the right result on a windy, chilly afternoon at the Fraser Eagle Stadium.
Accrington, clearly missing their Benin international Romuald Boco, were at their best in the opening 45 minutes.
However, they could easily have been behind before Andy Todd scrambled them in front 12 minutes before the break.
With his height and speed, but a distinct lack of skill, Fola Onibuje was a handful for the home defenders.
On the half hour he only had goalie Ian Dunbavin to beat, but a bad first touch led to a rushed shot and Accrington survived the scare.
Within a couple of minutes they were ahead. Ian Craney curled in a free-kick from the Stanley left, Paul Mullin's flick caused confusion in the Swindon defence and Todd poked home from close range.
In the second half Town were much improved and played like a team challenging for promotion. They hit the bar almost immediately after the re-start and Lee Peacock also had a goal disallowed for a push.
But Swindon continued to press and got their reward after 66 minutes. Onibuje used all the muscle in his 6ft 6ins frame to hold off Michael Welch. His persistence took him into the area and the final shot was only blocked by Dunbavin. Peacock was quickest to the loose ball and gleefully brought the Robins level.
Manager Dennis Wise went for the win by bringing on striker Christian Roberts and the former Bristol City man almost put the Robins in front, creating space for himself on the edge of the area before letting fly with a 20-yarder that went just wide.
Accrington have a habit of notching late goals, but even the introduction of super sub Andy Mangan couldn't break the stalemate as time ticked away.
Earlier on the kick-off was delayed for 15 minutes after the fourth official Colin Harwood suffered a family bereavement.
The sad news came at 2.30pm, causing referee Gary Sutton to appeal for a replacement. In the end Michael O'Keefe, a qualified official from Kent, who happened to be visiting the Stanley ground, took over Mr Harwood's duties.