Our exciting midfielder exchanged passes with Craig Bellamy before firing home across Italian keeper Gianluigi Buffon from a tight angle in the 12th minute of the Euro 2004 qualifier at the Millennium Stadium.
Allesandro Del Piero levelled with a deflected free-kick before the break but Bellamy won it with a fine finish after being released by John Hartson.
It was a tireless display by Simon who probed throughout, had another couple of shots in the second half and was named man of the match by BBC Wales.
He has now scored in his last three internationals against Croatia, Finland and now Italy. The win leaves Wales top of their group.
Elsewhere, Sergei Rebrov came on as a second half substitute in Ukraine's 0-0 draw in Northern Ireland.
Robbie Keane had few clear-cut chances in Ireland's home defeat against Switzerland, where Gary Doherty came on as a second half substitute.
Steffen Iversen, a goalscorer on Saturday, started in Norway's 2-0 victory against Bosnia-Herzegovina.
Simon Davies netted his third goal in as many internationals as Wales completed a famous win against Italy last night.