Referee Scott Mathieson allowed play to continue when Sam Mantom was fouled, and Paterson cut inside before rifling his seventh goal of the season into the roof of the net with a magnificent left-foot strike.
Walsall lost Florent Cuvellier and Andy Taylor with injuries during the first half when Stevenage looked sharper and Saddlers' keeper Karl Darlow - back at the Banks's Stadium for a second spell on loan from Nottingham Forst - did well to keep out one drive from Filipe Morais.
In the 35th minute Morais rattled the crossbar with a free-kick.
Walsall picked up their game in the second half and after a shot from Stevenage midfield man Anthony Grant was saved by Darlow, Will Grigg twice went close for the home side.
A key moment came in the 83rd minute when Boro sub Greg Tansley saw his goal-bound drive deflected for a corner and shortly afterwards Walsall drove forward to collect their third win in four outings.