Rahmon Fletcher scored 18 points and Joe Chapman 17 for the champions; TrayVonn Wright and Andrew Sullivan hit 14 points each for the Riders.
Leicester led by 14 points in the third quarter but found the Eagles' comeback irresistible in the last 10 minutes.
Sheffield Hatters beat Barking Abbey 79-45 in the Trophy final to continue their domination of the women's game.
The Hatters, led by Great Britain guard Helen Naylor's 21 points, scored the first 15 points of the game.
"Experience pays," noted Hatter coach Vanessa  Ellis. "We can bring people off the bench who are GB internationals [Steph Gandy and Olympian Julie Page] and that gives confidence to the team."
Newcastle are similarly dominant in the men's game and Sunday's victory means they remain unbeaten after 23 matches this season.
The Eagles and Riders, meeting in the final for the third time in the last four years, produced what Eagles coach Fab Flournoy called the "most intense final that I've been part of in the last 10 years" in front of a near-capacity crowd estimated at more than 9,000.
Leicester's ball control and defence edged the first quarter 28-25 and after trailing briefly at the start of the second, they reached half-time 50-41 in front.
Three point shots from Jamell Anderson, Tyler Bernardini and Wright studded an 18-8 Riders run to put Leicester 14 ahead in the third quarter but Newcastle surged back to retake the lead for good midway through the final quarter thanks to the efforts of Fletcher, Andrew Lasker and Scott Martin.
"It was frustrating, not so much about the loss but the way we conceded in the second half," said Leicester's Sullivan.
"Newcastle are the standard in this league but some of the mistakes we made allowed them to chip away at our lead."
Lasker said he had not been aware of how big Leicester's third-quarter lead was, just that "there was a lot of time left and you're never going to get it all back in one go".
He added: "We never panicked. We just played our style of basketball."
Newcastle Eagles won the BBL Cup for the fourth time when they beat Leicester Riders 94-82 in Birmingham.