The Foxes needed nine off Mitchell Starc's final over but could manage just four to fall to their fifth defeat in as many games.
By contrast Richard Pyrah clubbed 16 from Yorkshire's final over, launching Abdul Razzaq's first two deliveries over the rope, as the visitors posted 151 for nine.
Four run outs then undermined Leicestershire's chase before Australia left-armer Starc's impressive final over saw him remove Wayne White before bowling Nathan Buck with the final ball.
Herschelle Gibbs thrashed an unbeaten 83 off 58 balls as Durham beat Derbyshire by eight wickets with 17 balls to spare at Chester-le-Street. Late hitting from former Durham player Garry Park (29 off 20) helped Derbyshire to 131 for seven but it was not enough after Gibbs cut loose.
Paul Best claimed three for 19 on only his second Friends Life t20 appearance to help Warwickshire to a comfortable seven-wicket success over Gloucestershire.
The home side could post only 122 for seven after winning the toss, Dan Housego top-scoring with an unbeaten 59 off 61 balls and left-arm spinner Best proving the most penetrating of the Warwickshire bowlers.
The result was never in serious doubt when the visitors replied as Varun Chopra (56 not out) and skipper Jim Troughton (30) shared a second-wicket stand of 69 in 12 overs and victory was sealed with 11 balls to spare.
Sean Ervine hit his first domestic Twenty20 half-century in two seasons as Hampshire beat Middlesex by four wickets with four balls to spare. Ervine struck five fours and three sixes in his unbeaten 75 and brought up the winning runs with a boundary off Tim Murtagh.
Hampshire had been set a target of 157 after Paul Stirling batted through the innings to finish with 82 not out, which led the hosts to a total of 156 for two.