Manchester’s victory has now moved them into the top eight, while injury-hit Plymouth face a bottom four finish for the second year running.
Raiders, who were without Jordan Clarke and Louis Sayers and with Pierre Hampton and Brent Benson starting on the bench due to illness and injury, trailed 25-22 at the end of the first quarter.
However, the home team hit back in the second period to take a 51-49 lead before the Giants took control again in the third, leading 69-63.
The start of the fourth proved crucial for the Raiders, who went more than three minutes without a score. Manchester went 84-63 up and although Jay Marriott’s side hit back well they were unable to get any closer than two points.
Hampton, despite suffering with illness, topped scored in the game with 31.