Swindon had an early penalty appeal turned down when new signing Frank Nouble appeared to be fouled just inside the box.
It was Norwich who took the lead in the second half when on 52 minutes Grant Holt headed them into the lead in front of their 2,900 travelling fans.
Norwich could have made it 2-0 mid way through the secon half when they hit the bar.
However 2 minutes into stoppage time Swindon pulled a goal back to equalise when a Gordon Greer header following a corner to make it 1-1.
Overall a good game where a draw was a fair result. This leaves Swindon in 4th plave going into Saturday's away trip to Hartlepool.