Elwiss, The Blaze’s leading scorer in the competition was first injured in the field and then struck on the hand again while batting, but ignored the pain to strike nine fours in her 102-ball stay.
She shared a stand of 113 for the third wicket with Marie Kelly who made 69 in The Blaze’s 253-5.
Earlier, slow left-armer Maria Andrews marked her List A debut with an impressive 3-40 to restrict Surrey to 252-9, Jemima Spence (59) and Alice Monaghan (49) the chief contributors. Grace Ballinger backed up Andrews’ efforts with 3-49.
Second-placed Hampshire, meanwhile, registered their second highest ever List-A total to beat Somerset by 39 runs.
Francesca Sweet top-scored with 57 from 52 deliveries, while Rhianna Southby contributed 53 and Maia Bouchier 50 as Hampshire posted 303-7.
Spinners Liv Barnes and Lola Harris claimed 3-54 and 2-56 respectively, their performances the only highlight of a below-par Somerset showing in the field.
The home side made a good fist of chasing, Anika Learoyd and Bex Odgers scoring 87 and 77 respectively and staging a second wicket stand of 161 in 25 overs to threaten an unlikely outcome.
But Amanda Jade Wellington returned figures of 3-52 and Georgia Adams 3-45 as Somerset, well-placed at 199-1, were eventually dismissed for 264 in 46.3 overs.
Classy centuries from both Meg Austin and Katie George led Warwickshire to a 20-run victory over lowly Lancashire and a third straight success.
Austin (116) and George (127) put on 166 for the third wicket which, despite the excellence of Lancashire opener Eve Jones (113), proved a match-winning partnership as the visitors fell short on 294 in reply to the hosts’ 314-7.
In Saturday’s other game, Durham defeated Essex by 46 runs as teenage seamer Trudy Johnson wrecked the hosts’ top order with a three-wicket burst.
The 19-year-old finished with 3-28, including wickets in successive deliveries, to restrict Essex to 245 – 47 short of their target – despite half-centuries by Flo Miller and debutant Nancy Harman, signed on a short-term loan from Hampshire.
Earlier, a century partnership between former Essex all-rounder Mady Villiers, who struck 76 from 70 and visiting skipper Hollie Armitage, with 69 from 78, put Durham in control at 199-2.
Spinner Sophia Smale (4-51) pegged them back by dismissing both batters in quick succession but, despite losing six wickets for 56, Durham’s total of 291-9 proved to be adequate.
Match report details supplied by ECB Reporters’ Network, supported by Rothesay