The Royals seemed set for their 11th straight league defeat when the inconsistent Riders opened a 13-point first-quarter lead, but Hemel led 65-63 by the end of the third quarter and then outscored Leicester 17-5.
From leading 82-68, though, the winning touch looked like deserting them as it had at Derby earlier in the season, where they lost after leading by 16 points.
Riders came back to trail just 84-82 and the nervous Royals collected two technical fouls in the final moments before two free throws from the American, Allen Koochof, steered them to safety.
Thames Valley Tigers needed overtime to defeat Derby Bucks 100-94. Peter Scantlebury gave Tigers a
90-88 lead five seconds from the end of regular time, but Andy Gardiner rebounded a missed shot by Derby and scored to force the extra period. Michael Hayles, with four free throws, and Tony Holley, with two, scored Tigers' last six points.
Chester Jets also scored the last six points of their game but lost 84-74 at Guildford Kings, where the home team's Julio Politi scored four consecutive three-pointers in the final quarter.