Bradford led at half-time with a goal after 16 minutes from defender Rory McArdle following skipper Gary Jones' corner from the left-hand side. The Northern Ireland international scored with a header that went in off the underside of the crossbar.
However, Swindon deservedly equalised in the 63rd minute through Pritchard, on loan from Tottenham. The 20-year-old collected a ball on the right before weaving his way through the home defence and scoring with low, left-foot shot into the bottom corner of the net.
Both sides went close to snatching a winner in a frantic final 25 minutes. Swindon goalkeeper Wes Foderingham did well to keep out a volley from substitute Nathan Doyle in the 82nd minute while at the other end Jon McLaughlin made an equally good save to deny Robins sub Miles Storey in stoppage time.