I Cavalieri Prato came within four minutes of notching only their second European win after hitting back from a 12 point deficit in the final quarter.
Two tries in the space of six minutes from Nicolo Tempestini and lock Giacomo Bemini, both converted by Marco Frati, threatened to end their run of 12 straight defeats in the Amlin Challenge Cup, but it was not to be their day in the end.
Having led from the 11th to the 75th minute, London Welsh managed to work their way downfield and earn a long-range penalty with two minutes left on the clock.
Up stepped full back Alex Davies and over went his second penalty from 45 metres to regain the lead. That made it 32-31 and the Exiles hung on from there.
But the Italians at least ended with two points from the game having outscored their Pool 5 rivals by four tries to three, but they couldn't quite manage to emulate their famous 23-21 home win over Connacht two years ago on their first European outing.
Having been thumped 68-19 by Stade Francais Paris on their first foray into the Amlin Challenge cup last weekend, London Welsh were delighted to have picked up their first win in the tournament.
Hooker Dan George starter the scoring with a try after 11 minutes and wing Joe Ajuwa grabbed a try in each half for the visitors. There were five penalties split between Gordon Ross and Davies and Ross also converted one try.