Wes Durston smashed a rapid 50, but Derbyshire lost regular wickets in their chase of Birmingham's 189-5, which they reached thanks to 74 from William Porterfield, 35 from Varun Chopra and 50 from Jonathon Webb.
The Falcons were 143-6 before Alex Hughes smashed two sixes and two fours in a 10-ball knock of 24, and Tony Palladino and David Wainwright saw them over the line with three wickets and an over to spare.
Somerset made 150-7, with Craig Kieswetter top scoring with 40, and the Eagles, who had Mark Pettini star with 60 not out, were ahead of the rate on 125-2 after 16 overs when the wet weather arrived in Taunton.
Rain meant that there was no play between Worcestershire Rapids and Nottinghamshire Outlaws at New Road, or at Headingley, where Yorkshire Vikings were due to host Lancashire Lightning in the Roses derby.
The South got the better of the conditions, and Surrey revelled in them by thrashing Hampshire by eight wickets to knock the two-time winners off the top of the division, and climb to third themselves.
Sussex Sharks are one place behind the Londoners in the table, and also won convincingly at bottom side Middlesex Panthers, who were bowled out for 107, with Lewis Hatchett and Will Beer claiming three wickets apiece. Chris Nash thumped an unbeaten 74 as Sussex made quick work of knocking off their modest target.
Rouse top scored with 35 off 16 balls, coming in at number seven, as the home side just managed to knock off Kent's total of 150-6, in which Sam Northeast starred with 75 from 49 balls.
Gloucestershire (154-7) beat Kent Spitfires (150-6) by three wickets.
Essex Eagles (125-2) beat Somerset (150-7) by eight wickets (D/L).
Worcestershire Rapids vs. Nottinghamshire Outlaws - no result.
Yorkshire Vikings vs. Lancashire Lightning - no result.
Durham Jets (69-4) vs. Northants Steelbacks - no result.
Surrey (137-2) beat Hampshire (131-9) by eight wickets.
Sussex Sharks (110-4) beat Middlesex Panthers (107 a/o) by six wickets.
Derbyshire Falcons (193-7) beat Birmingham Bears (189-5) by three wickets.