Somerset had looked set to record a fourth successive victory in the competition after impressive contributions from Peter Trego (118), Alviro Petersen (63 not out), Marcus Trescothick (57) and Jos Buttler (54no) led them to 323 for three.
However, Cobb and Smith launched a stunning assault on the Somerset attack as Leicestershire won by six wickets at Grace Road. Cobb made 130 off 87 balls while Smith finished unbeaten on 135 off 109 deliveries as the home side eased past the finishing line with seven balls to spare to make it two wins from two in Group C.
In the same group, Gloucestershire beat winless Unicorns by 29 runs at Bristol. Half-centuries from Benny Howell, Michael Klinger and Ian Cockbain guided Gloucestershire to 260 for seven and Unicorns could only make 231 for five in reply, despite 76 from opener Tom Lancefield.
Nottinghamshire continue to blaze a trail in Group A after beating Holland by 89 runs for their fifth successive victory in the tournament.
England trio Michael Lumb (54), James Taylor (75) and Samit Patel (61) led Nottinghamshire to 263 for five batting first at Trent Bridge, and another of their international contingent, Ajmal Shahzad, then took three for 26 as Holland were bowled out for 174.
Sussex and Northamptonshire were also victorious in Group A. Sussex beat second-placed Kent by 20 runs at Horsham after bowling their opponents out for 202 in the final over.
Chris Jordan played a key role with bat and ball for the victors, contributing an unbeaten 37 in a score of 222 for nine and then claiming two for 36 - including the vital scalps of Darren Stevens (51) and Ben Harmison (42) - as Kent fell short.
Northamptonshire, meanwhile, were celebrating their first win after defeating Worcestershire by 42 runs at New Road. Steven Crook's quick-fire 61 not out led Northants to 219 for six and Matthew Spriegel (three for 29) and David Willey (three for 28) then helped dismiss their hosts for 177 despite 78 from Sri Lankan star Thilan Samaraweera.
In Group B, unbeaten Derbyshire picked up a second win after seeing off last-placed Scotland by six wickets in Edinburgh. Mark Footitt finished with superb figures of five for 28 as Scotland made 182 for nine after opting to bat, and Derbyshire rarely looked in danger of falling short after openers Chesney Hughes (74) and Shivnarine Chanderpaul (54) had put on 120 for the first wicket.