The visitors came into the North Group match having won four of their last five completed games, and they then compiled a formidable total after being put in by the Foxes on a good pitch.
At 98-0 after eight overs, it looked as though the visitors might even threaten the record T20 score made against Leicestershire, 225-2 by Durham at Chester-le-Street in 2010.
Alex Hales, fresh from his destructive century off 45 balls in the previous game against Yorkshire, raced to a half-century off 26 deliveries, while Riki Wessels needed only three more balls to go to his own fifty, the highlight being a 97-metre six over wide long leg that flew out of the ground and into the garden of a nearby house.
The introduction of the off-spin of Colin Ackermann slowed the assault, however, not least because he quickly had Hales (51) stumped off a wide delivery.
Spin was also responsible for the fall of the next two wickets, with left-armer Callum Parkinson (2-39) having Tom Moores (19) taken at long-on thanks to a good low catch by Aadil Ali, and in the same over dismissing Wessels, who had reached 63 when he top-edged an attempted reverse sweep and was held by Clint McKay back-pedalling from short third man.
The Foxes' bowlers continued to peg the Outlaws back and in the 14th over Brendan Taylor and Samit Patel were bowled for golden ducks by successive deliveries from South African left-arm seamer Dieter Klein (2-41).
And in the end it needed Dan Christian's 33 from 22 balls to see the visitors past 200.
But rain had been falling intermittently throughout much of the latter part of the innings and it became steady in the final over, causing a 90-minute delay.
It relented sufficiently for the umpires to consider a restart, with Leicestershire's Duckworth-Lewis target a daunting 68 off five overs, but the rain returned just before the players were due back on the field.
