The Pool One table-toppers gained maximum points in a ten-try thriller and need to win at Italian minnows Benetton Treviso next weekend to reach the quarter-finals.
The Exiles No.8 opened the try-scoring after 12 minutes and added further tries in the 46th and 76th minute at the Madejski Stadium.
London Irish director of rugby Brian Smith said: "Richard has come through the academy system and has repaid our faith. He's not played regularly for us but he has stepped up and taken us all by surprise."
Eoghan Hickey, Shane Geraghty and Peter Hewat all touched down before the break to hand the Guinness Premiership the all-important bonus-point within 36 minutes.
The Dragons had scored by then after a momentarily lapse in concentration by wing Topsy Ojo allowed wing Richard Fussell to score in the left corner. But following Thorpe's second score after the interval put the hosts 34-7 clear, the visitors rallied with tries by Ben Daly, Gareth Wyatt and Ceri Sweeney before Thorpe had the last laugh.
Dragons Coach Paul Turner said: "We can't get things so wrong defensively and expect to win games.
"Our first half was unacceptable so we gave the players an old-fashioned team-talk at half-time and they responded in the second half."