It was a frantic opening 20 minutes with both sides having half chances, but neither stopper was forced to make a meaningful save.
The home side broke the deadlock when Forsythe beat his marker and leapt to connect with Jarlath O'Rourke's corner.
Glentoran nearly cancelled that strike out instantly after Jonny Tuffey made a good save to deny a goal-bound header from Danny Amos. However, David Fisher was able to control the rebound with his effort cleared off the line by Jimmy Callacher.
Dylan Connolly and Amos then fired off target as a half of few chances drew to a close.
The start of the second half followed the same pattern, with chances at a premium and Daniel Larmour's effort from the edge of the box being gathered by Daniel Gyollai the first chance after the restart.
Offord then weaved his way round multiple white shirts after connecting with Jordan Stewart's cross, but sent his resulting strike just wide.
Declan Devine's side levelled the game when Callacher's attempted clearance of Aaron Wightman's delivery fell to Jenkins and he cleverly chested the ball down before poking home.
Glentoran took the lead just three minutes later after Wassim played a one-two with Jenkins and delivered the ball to the edge of the box for the onrushing fellow Lindsay, who sent a curling strike over stopper Tuffey.
Crusaders then had a huge chance to level the game, but Philip Lowry was unable to nod home Ross Clarke's header.
Glentoran sealed the three points as Wassim got on the scoresheet himself after Jenkins' effort was palmed away by Tuffey and the predatory Glens player was able to convert the rebound from point-blank range.