The Sharks lost their impressive Italian-American, Matt Gaudio, early in the second quarter when he limped out of the game with a knee injury. But Iain McKinney's fifth three-pointer, 71 seconds from time, gave Sheffield hope of defending their unbeaten run by cutting Derby's lead to 83-82.
Derby's John Tresvant then missed, but his team-mate Maurice Robinson reacted fast and scored to put the Storm 85-82 ahead.
Travis Conlan missed a three-point attempt and fouled Yorrick Williams, who scored both free throws 13 seconds from time, before Conlan scored a three-pointer with the game's final shot.
Following Friday night's 88-81 victory at Newcastle Eagles, yesterday's win pushed Derby into third behind Manchester Giants and Sheffield.
Giants were missing their former Leopard, Makeba Perry, but John White's 28 points, and 24 from Tony Dorsey, led Manchester to a 110-82 win over Chester Jets, while Chuck Guittar top-scored with 21 in Birmingham's 79- 66 victory over winless Edinburgh Rocks.
Malcolm Leak scored 31 in London Towers 101-81 win over Greater London Leopards, and Jason Siemon hit 31 in Thames Valley Tigers' 120-80 victory at Worthing Bears.
Mind games paid dividends for Leicester City Riders, who beat Milton Keynes Lions 82-75 for only their third win of the season, after their coach, Dave Harris, and his players had sessions with a psychologist in the run-up to the game.
Harris, in his first season as a head coach, threatened to bring in new players if the Riders did not increase their tempo from the start of the game. They responded by taking a 20-14 lead.
Riders stretched that to 56-39 in the third quarter before a 14-3 Lions run dragged them back to 79-72. JaRon Boone, 25 points, and Hilroy Thomas made the game safe with four free throws.