Lancashire's grim 3 for 2 start - Tim Munton dismissed Graham Lloyd and John Crawley, both without scoring, in the first over - was rescued by Fairbrother and Stephen Titchard who put on 89 in 21 overs.
After Fairbrother was fourth out for 70, with eight fours and a six, Munton enjoyed a less fruitful finale. He was hit for three straight sixes by Warren Hegg in an over that cost 25 runs.
Warwickshire were always struggling, also losing a wicket in the first over, and as Gary Yates took 4 for 34 they were all out for 111.
Yorkshire could have headed the table but fell foul of Kent's little-used Tim Wren. In his fourth game in as many years he took three wickets in four balls as Yorkshire crumbled to 54 for 5. That they reched the giddy heights of 165 for 8 was due to Paul Grayson (55) and Peter Hartley (35).
The total was put into context when Trevor Ward (two sixes and seven fours) and Carl Hooper hit half-centuries and Kent's fourth win of the season came by eight wickets.
Nottinghamshire were also denied a place at the top. They succumbed to Northamptonshire's first win of the season - by one wicket, and with a boundary off the last ball at that. For that they can thank David Capel. Batting with a runner he scored an unbeaten 29 off only 12 deliveries for the unlikely victory.
Phil Simmons continues to enjoy himself on a Sunday. First came a rapid 51, his third fifty in a row, with six fours and a six in Leicestershire's modest 161. With the ball he took 4 for 19 in four overs as Essex were bowled out for 147.
The wicketkeeper Paul Nixon took six catches to equal the league record set by Derbyshire's Bob Taylor in 1975.
There were two more wins off the final ball. Ottis Gibson hit Courtney Walsh for six to give Glamorgan, the champions, their third win in a row and at Taunton, Worcestershire's Neil Radford also struck a six to win the game.Reuse content