Put in on a grey morning with the floodlights shining brightly, Surrey started briskly, scoring 19 from three overs, but Paige Scholfield missed a drive at Charley Phillips and was bowled off-stump.
Alice Monaghan then lifted a pull at Lucy Higham and was well caught by Tammy Beaumont at square leg.
Gordon then left Surrey reeling with three quickfire wickets – Bryony Smith top-edged to deep square leg and Alice Davidson-Richards and Jemima Spice were both bowled.
From 57-5, Surrey had little option to retrench and Kira Chathli (28) and Chatterji added a watchful 36 before the former was adjudged leg-before to Josie Groves.
Less arguable was the lbw call against Aylish Cranston (20) when she missed a sweep at Higham and Chatterji, having hit just two fours in a diligent innings that at least gave her side something to bowl at, was caught at long on off Kathryn Bryce who then had Danielle Gregory caught at point.
When England newcomer Tilly Corteen-Coleman was yorked by Phillips, Surrey’s innings ended with 42 balls unused.
Their bowlers, though, responded impressively with three wickets in the first five overs as Corteen-Coleman had Beaumont caught at slip, and Maitlin Brown bowled Kathryn Bryce and Amy Jones to leave The Blaze 19-3.
Elwiss and Sarah Bryce (29) added 42 but Monaghan powered Surrey back into the match by hitting the off-stumps of Bryce and Ella Claridge with successive balls.
Elwiss and Emma Jones were unruffled and the former hooked Brown for six to bring up the 100 as the sixth-wicket pair added 50 from 75 balls.
Elwiss reached her half-century from 72 deliveries and well though Surrey bowled, their batters’ under-performance had left them too much to do as the sixth-wicket pair closed out an ultimately comfortable victory with 93 balls in hand.
“I think maybe another 40 or 50 runs, setting them 200, and it would have been a very good game. It was a great effort to try and claw it back but we just couldn’t get over the line,” said Surrey skipper Chathli.
“This is a testing time for us. It is a just a matter of how well we can regroup as a team. We have just got to keep backing ourselves and believing we can do it and we’ll soon be back on that winning streak.”