Tony Dorsey, Giants' leading scorer, managed only seven points in the first three quarters. But he hit 13 in the fourth including the free throws which put them 78-77 ahead and the three-pointer which stretched their lead to 81-77 after Chester's Dave Gardner missed two free throws and the chance to regain the lead.
Phil Handy's free throws made the game safe for Giants before Terrence Lewis scored a three-pointer for Chester with the game's final shot.
Thames Valley Tigers, who have won the trophy a record four times, were first to book their semi-final place in the opening game by inflicting a seventh consecutive defeat on London Leopards.
Leopards were outscored 14-4 over the final five minutes to lose 91-84 as their wasteful back court of Jason Kimbrough, Kenya Capers and Rashod Johnson combined for only 15 hits from 51 attempts.
Billy Singleton, Greg Meldrum and Tony Christie shouldered the load for Tigers as starting centre Jason Siemon was kept on the bench for 28 minutes by foul trouble.
With Leopards leading 80-77 and Siemon back on the bench, Christie stepped up to score nine of Tigers' last 14 points to leave London facing a bleak second half of the season.