Towers, the Budweiser league leaders, trailed 42-43 at half-time against the 10th-placed underdogs Leicester, then conceded the first six points of the second period to trail by 15.
Furious Towers' coach, Kevin Cadle, called a time-out after just 43 seconds and his players responded with a 22-2 run over the next five minutes to take the lead at 55-50.
But the Riders, with American JaRon Boone in sparkling form from three- point range, fought back to take the lead again at 58-57. The teams traded baskets until James Hamilton scored a single free throw three seconds from time to snatch the narrow win for Towers.
Gene Waldron and Billy Singleton, with 14 points each, supported Boone and the Riders now have a strong chance of reaching their first final since losing to Sunderland in 1991.
Danny Lewis led London scorers with 15 points ahead of Keith Robinson on 13 and Italian Marco Baldi with 12.
Thames Valley Tigers lead Birmingham Bullets 63-55 after the first leg of their semi-final, played on Wednesday.
Chester Jets have signed American forward John Tresvant, who will make his debut in Sunday's League Trophy qualifying group game at home to Leicester.
Tresvant won a league championship medal last season with Greater London Leopards, but was released last week when they signed the American guard Ryan Cuff from Worthing Bears.
The Jets have three Americans on the injured list, Sean Bell, Brian Lloyd, and Ricardo Leonard.
Leonard, who will have an exploratory knee operation on New Year's Day, will play against Leicester but Lloyd (hairline ankle fracture) and Bell (injured knee) are both out.