Playing their first game at a major championship since the 1958 World Cup, Wales took a 10th-minute lead courtesy of Gareth Bale’s fine free-kick, only for Slovakia substitute Ondrej Duda to equalise.
But with nine minutes remaining, Robson-Kanu, released by Reading at the end of the season, scuffed a shot past Matus Kozacik to send Chris Coleman’s side striding towards the last 16.
His strike ended Wales’s four-game winless run and tees the European Championship debutants up perfectly for Thursday’s hotly anticipated second Group B fixture against neighbours England in Lens.