The win means last year's wooden spoon side is assured a top-two finish in the regular season with a game to play.
With Steve Robinson and Jason Frost unavailable, the Bombers turned to the veteran presence of forward Max Jablonski (16 points) and centre Chris Hepburn (15).
With first-choice point guards Richie Rodger and AJ Auld-Beverley also out of action, Jade Shaw ran the offence efficiently from the point.
With a colossal height advantage for the Bombers, Shaw was able to feed his big men inside and let them power to the hoop. Otago Boys' sorely missed Sam Timmins and Joe Cook-Green at both ends.
The schoolboys were comprehensively out-rebounded and struggled to gain any ascendancy in the paint.
As a result, they had to settle for too many low-percentage shots, including 24 three-pointers. Scott Adler scored a game-high 23 points, including two first-quarter three-pointers, as Otago Boys led for the majority of the first quarter.
However, Gillies drained a three-pointer and Hepburn landed a hook shot to give the Bombers a 22-21 lead after the first 10 minutes.
The Bombers opened up a nine-point buffer late in the first half, before Adler and Josh Petermann made three-point plays to close the gap to two points. Hepburn finished the half with a pair of free-throws to give the boys in green a 37-33 lead.
While Adler opened the second half with a layup to pull Otago Boys' to within a basket, the Bombers responded with a frenzy of baskets.
A 12-0 run opened up a 49-35 lead and prompted an Otago Boys' time-out. Following the break, the school side stopped shooting outside jumpers and started attacking the basket.
The change of approach helped as it closed the deficit to 12 points with a quarter to play. However, Gillies scored seven quick points to open the fourth quarter and the Bombers romped home down the stretch.
Gallaher and Stirling benefited from some superb passing under the basket, while Gillies was devastating attacking the basket.
In the other games, Nuggets guard Micah Lepaio exploded for 41 points in a rare appearance for the Magic (5-9) as they thumped Varsity A (3-11) 100-76.
Varsity forward Sam King scored 32 points in the loss and has now notched up 97 points in his three appearances this season. Earlier, James Ross scored 23 points as the St Kilda Saints (11-2) made light work of Falcons A (5-7) 92-74.
It was the sixth straight win for the streaking Saints and it all but sealed the top seed with one regular-season and one deferred game to play this week.
By Robert van Royen.
