A Sam Smith brace had Reading 2-0 up inside the opening half-hour.
But Savvas Mourgos scored for the visitors with a superb free-kick shortly before half-time.
Norwich levelled when Cantwell (pictured above) struck an 89th-minute penalty after Axel Oskar Andresson had been sent off for a challenge on Glenn Middleton.
It means Reading must settle for third ahead of their next match, at Middlesbrough, on 15 October.
Norwich climb to ninth and next host West Bromwich Albion on the same day.