The full-back - playing on the left of three central defenders for Wales - produced a fantastic clearance off the line in the early stages as Wales won their first match in the European Championship finals, their first major tournament since 1958.
Slovakia playmaker Marek Hamsik, who plies his trade at Napoli in Italy, broke from deep into the box and slid the ball past goalkeeper Danny Ward only for Ben to race back and save a certain goal.
Below: Ben saves the day for Wales
Gareth Bale opened the scoring as Wales had the better of the first half, Ondrej Duda levelled on 58 minutes in Slovakia's best spell but Wales hit back and won it through Hal Robson-Kanu with 10 minutes left.
Ben completed the 90 minutes and legendary Welsh striker Dean Saunders, part of the BBC MOTD team, said his clearance 'would live long in the memory' if Wales progressed further.
England are next up for Wales in Group B in Lens on Thursday (2pm UK).