The Riders appeared to have the edge, leading by five with 1:31 to play, but Sheffield levelled with the final five points to leave the tie evenly poised.
Jerrold Brooks netted seven triples in his 24-point haul, while Antone Robinson went 9-of-12 from the field for his 20 points, including the crucial game-tying basket in the final 20 seconds.
Sheffield will have home advantage in the second leg on Wednesday with the winner securing their place in the BBL Trophy Final at the Emirates Arena.
There was nothing to split the two sides at the end of the first, and the Sharks would just have their noses ahead at the half following a 11-4 close.
Leicester started the third period the stronger of the two sides and led by as many as seven points at 61-54. The home side had been ahead since over eight minutes to play in the third, and looked well placed with a 79-74 advantage with 90 seconds to go.
However, Mike Tuck and Brandon Hogg went a combined 3-of-4 from the line, and Robinson levelled following a steal/assist from Hogg.
Neil Watson’s potential game-winner rimmed out at the buzzer as the game finished as a draw.
TrayVonn Wright recorded a double-double for the Riders with 22 points and 10 rebounds with his side now needing to win in Sheffield to reach the BBL Trophy Final for the second year running.