At the Utilita Bowl, Hampshire posted 259-8 from their 50 overs, with an opening-wicket partnership worth 116 between Ella McCaughan and Maia Bouchier putting the hosts in a strong position at the halfway stage.
Alice Capsey top-scored for Surrey with 57, but when she was caught by Hampshire captain Georgia Adams off the bowling of Freya Davies with just two wickets left, slim chances of the visitors reaching a total of 260 had faded and the Brown Caps were eventually bowled out still 50 runs short.
In Chelmsford, a superb career-best knock of 130 from Warwickshire’s Emily Arlott helped the Bears post a target of 290 from their 50 overs.
In reply, Essex made a good start and remained in with a shout at the fall of the fourth wicket, but the loss of six wickets for just 43 runs meant Warwickshire romped home to an 108-run victory.
The Blaze got their first win of the campaign when they chased down Durham’s target of 201 with five wickets remaining at Chester-le-Street.
Kathryn Bryce top-scored for the East Midlands-based outfit with 54 as the visitors eased home with more than 12 overs left.
Spin-bowler Sarah Glenn grabbed three wickets, while all-rounder Bryce, Grace Ballinger and Josie Groves shared two wickets each in a dominant victory.