The Warriors had not won in 12 Aviva Premiership outings in England prior to the game and had only the 9-9 draw in Oyonnax in the first round in Europe to point to for any success.
They managed to beat Cardiff Blues at the Arms Park in the Anglo-Welsh tournament, but this was their first competitive success at Sixways this season.
The relief for the 6,180 crowd was obvious, and the smile on the face of head coach Dean Ryan enormous, although there were some nervous moments at the death as they did all they could to hang on to their lead.
Record-breaking win for Cardiff
Oyonnax may be in their first season in the top flight in France, but they have picked up a number of notable scalps along the way and arrived with two wins and a draw from their five pool games in Europe.
Jonathan Bousquet gave them a ninth-minute lead with a penalty and then Salim Tebani crashed over for the first try of the match.
The Warriors kept their composure in difficult conditions and by the break a penalty try, converted by Ignacio Mieres, had brought them back to within one point.
Oyonnax lost Ruaan du Preez through a yellow card early in the second half and finally succumbed to the home pressure just after the hour.
Mieres landed two penalties within the space of four minutes to grab the lead and from then on it was a case of managing the lead.
Home prayers were answered a minute later when Max Stelling crossed for a try and Mieres' conversion made it 13 points in the space of six minutes.
That was game-changing and, even though Oyonnax hit back with a try by Bousquet eight minutes from time, the Warriors wound down the clock and thoroughly deserved what they got in the end.
London Irish ran in seven tries in their 49-0 hammering of I Cavalieri Prato in Italy, but it was not enough to enable them to overtake table-topping Stade Francais, who moved into the quarter-finals.
The Exiles got off to a flying start with a try in the first minute from Matt Parr, the first of four in the first half that secured the bonus point.
Declan Danaher, Andrew Fenby and Blair Cowan grabbed the other tries.
There were three more after the break to take the Exiles' total in the pool to 41 over the six games.
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