The latest in this long line of victories came at the Stoop as they brushed London Welsh aside 23-6 in the LV= Cup.
This all but guaranteed their safe passage into the final four and they need just two points or Northampton Saints to win at Sandy Park 24 hours earlier to do exactly that.
However, the history books suggest that is easier said than done with Ospreys winning all four of the previous meetings between the two sides.
And lock Matthews is adamant Quins will be leaving nothing to chance this weekend in Wales.
"To be honest I didn't even know we needed a draw, it's not something we considered," he said. "We play every game to win and the Ospreys clash this weekend will be no different.
"A trip to Wales is always tough but this team have proved that we are up to the job of going there and getting the result.
"It's a squad of 45 people, not just the 15 who are lucky enough to play on the weekend and we have so many young players who can come in and cover.
"We won the A League and the LV= Cup has been a great experience for us as well and hopefully that can continue against the Ospreys this weekend."
While Quins have their sights on a last-four spot in the LV= Cup, Ospreys' own hopes might be over by the time to take to the field if other results do not go their way.
Ospreys are winless in their last three encounters but have lost just one of the four previous LV= Cup ties that have taken place at Bridgend.
And head coach Steve Tandy believes his side are ready to keep the good times rolling in their home away from home.
"Harlequins will provide a really difficult test for us," Tandy said. "They aren't top of the Premiership and current champions, and top seeds in Europe for nothing.
"They have a quality squad and come to Bridgend looking for a result that could see them through to the top four so it's going to be a good game.
"It's a challenge but our preparation for the game has been good, the players know what is expected of them and that they need to be at their best if we are going to get the level of performance needed to get anything out of this match."