The Scottish outfit ran out 25-13 victors in their top-versus-bottom Pool 4 clash at Murrayfield last week, and repeated the trick with a comfortable 24-6 success at the Kassam Stadium on Sunday.
London Welsh are enduring a miserable season, having failed to win a game either in Europe or the Premiership, and they never looked like bucking that trend against an Edinburgh side out to make it four victories from four Challenge Cup outings.
Justin Burnell's side led 13-6 at half-time of last week's encounter before Edinburgh hit back, but a trio of Sam Hidalgo-Clyne penalties put the Pro12 team in control at 9-3 up at the interval this time around.
Hidalgo-Clyne picked up where he left off after the restart too, adding another three points in the 46th minute.
Chris Elder notched his second penalty of the afternoon soon after to bring London Welsh back within six points of the visitors.
But Edinburgh's class told thereafter, with winger Dougie Fife crossing for the game's opening try shortly before the hour.
Roddy Grant added a try of his own three minutes from time before Greig Tonks marked his 50th Edinburgh appearance with the conversion.
The victory keeps Edinburgh five points clear of Bordeaux-Begles at the top of Pool 4 ahead of the festive break, while London Welsh remain rooted to the bottom of the standings.