Afterward the game Edwards said the victory was partly inspired by the death of Ray Gravell, the Scarlets' president and Wales centre who had his funeral service at Stradey Park 48 hours before.
Before kick-off a wreath was laid in the middle of the pitch in Gravell's memory.
Edwards said: "It was our best performance of the season without a shadow of a doubt and against a very good side.
"The biggest sign of respect we could have paid Ray was to come here and play some hard-nosed tough rugby, just the way he liked it with no quarter asked and no quarter given."
Wasps director of rugby Ian McGeechan said: "We said that away wins are hard to get in this group so to get a five-point away win is a tremendous performance and credit the players."