The Rocks narrowly lost to their Tyneside rivals 96-91, despite their key American playmaker Jordan Johnson being out through injury.
Bunyan - the Rocks captain - came into the starting line-up and made a huge impression with 21 points in the first half to help Rocks stay in touch at 55-49 in a high scoring contest, after trailing by 18 points following the first quarter.
Fellow former Fury star Ali Fraser, who is heading for ankle surgery in two weeks’ time, managed to play the final three quarters and grab 18 points.
The third ex-Fury star in the Rocks line-up, Fraser Malcolm, also had a solid game with 10 points meaning the Falkirk trio had 53 of Rocks’ 91 points, a great showing in a league dominated by American-born players.
Bunyan also grabbed seven assists and will look to continue the form that has seen him rise to second top in the British Basketball League's three-point shooting percentage at 51%.
Rocks, who had also lost 90-77 at Sheffield Sharks on the Friday, travel to Newcastle this Friday in the Championship and then on Sunday play league leaders Leicester Riders at the Emirates Arena in Glasgow from 6pm.
Meanwhile, last weekend also saw Fury cadet men win 82-67 at Dundee in the Scottish U16 Division 1 League.
Top scorers in coach Ewan Carlow's side were Alec Low with 21 and Jack Shand on 18 points.