The pint-sized Robins appeared to have set City on course for their 20th league win of the season when he opened the scoring three minutes into the second half.
But their hopes of moving up to fourth place in the table were dashed by a 65th minute equaliser from Swindon's top scorer Sam Parkin.
Robins put City in front with a close-range header after winger Scott Murray, rated at £1milllion by Wilson, had crossed from the right but striker Parkin ensured mid-table Swindon, who themselves harbour outside hopes of making a late charge towards the play-off places, from slumping to a fourth defeat on the trot.
The former Chelsea striker rammed home his 21st goal of an increasing prolific campaign from eight yards out after striker partner Danny Invincibile had seen his shot parried by City keeper Steve Phillips.
City had the better of the first half with Robins and the impressive Lee Peacock both going close to breaking the deadlock early on.
Robins should have scored in the 15th minute when, with only Swindon keeper Bart Griemink to beat, he somehow volleyed wide from 12 yards out.
Swindon defender Alan Reeves had the home side's best first half-chance when he headed against a post in the 20th minute.
And Andy King's side will claim they looked more likely to win the game after Parkin's equaliser with captain Andrew Gurney sending a blistering 25-yard free-kick against the City crossbar late on.
But in the end a draw was a fair result and the majority of Swindon's biggest crowd of the season, 8,629, were sent home happy after a match which was delayed 15 minutes by crowd congestion.