Devon had overcome Gloucestershire 32-24 away the week before, but Surrey, whose squad is built around players from nine-times Premiership champions Richmond, were a difference class.
The visitors out-scored Devon eight tries to one, with five of their scores coming in the first half.
Devon, who included six Plymouth players in their matchday squad, did have some good spells and did ask a few questions of Surrey.
The home team did lead for 10 minutes in the first half following Goddard’s 70-metre uphill effort on nine minutes, but eventually Surrey’s strength and support play told.
Zoe Smith (2), Laura Kapo, Sam McCarthy, Libby Pavey, Vicky Boothman, Fran Hall and Kirsty Lee-Griffiths scored tries for Surrey.
Devon will complete their pool games next weekend when they travel to Berkshire.
Devon: 15 Lauren Mueller (Topsham), 14 Dawn Latham-Mahoney (Topsham), 13 Megan Higgins (Plymouth Albion), 12 Caitlin Short (Plymouth Albion), 11 Lilly Goddard (Plymouth Albion), 10 Charlotte Green (Cullompton), 9 Charley Wright (Cullompton), 1 Donna Downes (capt, Plymouth Albion), 2 Claire Knighton (Cullompton), 3 India Chambers (Withycombe), 4 Tilly Higgie (Plymouth Albion), 5 Charlotte Harvey (Topsham), 6 Gemma Parish (Cullompton), 7 Amy Alford (Cullompton), 8 Liz Richards (Cullompton). Replacements: 16 Chloe Dawe (Plymouth Albion), 17 Elena Wallis (Newton Abbot), 18 Corinne Walsh (Topsham), 19 Natasha Currie (Topsham), 20 Sophie Kukor (Topsham), 21 Rachel Popham-Dowle (Topsham), Emily White.