Mark Hardinges' dismissal secured the visitors a second bonus point to put them out of Gloucestershire's reach in the table.
Alan Richardson and Jamie Dalrymple took four wickets apiece as Middlesex limited the hosts to 333 all out. Malinga Bandara top-scored with 70.
England kept their hopes of completing a Test and one-day double over Australia alive by levelling the NatWest Women's Series with a four-wicket win at Taunton. Claire Taylor's century saw England reach their target of 216 with nine balls to spare, squaring the series at 2-2 heading into tomorrow's decider.
Taylor made 116 from 133 balls before she was bowled by Cathryn Fitzpatrick with only five runs needed. She received valuable support in half-century stands with the opener Laura Newton (31), Arran Brindle (23) and Jenny Gunn (32), but it was left to Jane Smit to hit the winning run in the penultimate over.
Gunn and Connor had earlier taken two wickets apiece as Australia were restricted to 215 for 5 after winning the toss and electing to bat.
Matt Prior made an entertaining 69 from only 50 balls as Sussex Sharks took another step towards promotion to the First Division of the totesport League by crushing Scottish Saltires at Hove yesterday.
The hosts, set only 133 to win, romped home by seven wickets with 21.1 overs in hand.
Prior, who presented Paul Hoffman with a difficult caught-and-bowled chance on 28, hit 13 fours and a six. Prior shared an opening stand of 99 runs in 13 overs with Richard Montgomerie before he was caught at fine leg.
Montgomerie steered Sussex towards victory with an unbeaten 35 from 45 balls and Mike Yardy struck the winning run by pushing Ross Lyons for a single.
Sussex can now virtually secure promotion with an 11th win at the expense of Surrey Lions under the Hove floodlights tonight.
The Pakistan pace bowler Rana Naved took a competition-best 5 for 30 in nine overs to restrict the Scots, whose modest innings was built around a steady 51 by the captain, Jon Beukes.Reuse content