Travel-happy London Welsh made it four wins out of four on the road this season with Saturday's 20-9 victory at Newbury.
They led by just a single point at half-time, thanks to Tom Tombleson's try and the first of two penalties from Aled Thomas. Welsh were really made to dig in after the break, but the home side failed to turn pressure into points.
And it was only when they were awarded a penalty try with two minutes left that the Dragons could breathe easy.
Welsh return to Old Deer Park on Saturday to welcome Esher.