The home fans celebrated boss Chris Wilder's decision to stay at The Shay with their best performance of the season.
The Shaymen have had a poor start to the campaign after last season's play-off final appearance but this second win of the season could prove a catalyst, just a week after Wilder turned down a switch to Conference rivals Cambridge.
The Daggers were hardly in the game and only a penalty early in the second half gave them brief hope but this game was all about Halifax.
Left-back Jake Wright finally broke the deadlock four minutes before the break and Ryan Sugden pounced on the stroke of half-time.
Dave Rainford pulled one back from the spot early in the second half but that did not knock Halifax out of their stride and Forrest smashed home into the top corner midway through the second half to seal a first home win.
The scoreline could have been more convincing had Halifax taken more of their chances in a first half they completely dominated.
Scoring goals has been a problem all season and the Shaymen hit the woodwork three times before they finally broke the deadlock.
It was literally one-way traffic with Dagenham never in the opening 45 minutes. Since the start of the season the likes of Adam Quinn, Tyrone Thompson and Sugden have been out-of-form but here all 10 outfield players were back to their best.
Thompson and Sugden had early efforts before a corner routine had the Daggers rocking. A Wright flag-kick was met by Greg Young whose header was pushed out by Tony Roberts.
Wright collected the ball again and Quinn rose to thump a header off the crossbar and Andy Campbell was first to the rebound and was about to celebrate but saw his shot come back off the far post.
Defender Jake Leberl almost gifted Halifax the goal they needed when he headed Sugden's flick past his own keeper and was relieved to see it roll past the post as well.
Referee Russell Fletcher played the advantage when Lewis Killeen was flattened on the edge of the box but Sugden's lob struck the top of the bar.
Martin Foster dragged his shot wide after a power-packed forward run but it was all the home side.
The nearest Dagenham came was when Quinn's misplaced back-pass left Craig Mawson exposed and he was forced into a desperate last-ditch clearance.
Just when it seemed Halifax were set to go in at half-time without reward Wright, Foster and Gus Uhlenbeek produced a 25-yard free-kick straight from the training ground.
Uhlenbeek shaped to take it but dummied leaving Wright to nudge it to Foster and then peel away and smash home from the edge of the box.
The home fans, in good heart throughout, couldn't quite believe the intricate move had worked and, on the stroke of half-time, Halifax doubled their lead when Forrest, restored to the right wing, delivered a great cross and Sugden slid in to turn it over the line.
After the break Dagenham, with nothing to lose, came back at Halifax with Craig Mackail-Smith trying a lob which Mawson always had covered.
Mawson, though, was forced to bring down Cliff Akurang when he broke into the Halifax box. Rainford stepped up and Mawson went the right way but could not keep the ball out.
Halifax refused to be shaken and continued to attack with Campbell, now fully fit after missing pre-season, showing pace and a willingness to run at defenders.
Forrest clinched the victory in the 73rd minute when he cut inside from the right and launched an unstoppable shot which Roberts could only get his fingertips to as it smashed into the top corner.
Roberts then produced a brilliant point-blank save from Forrest as Halifax threatened to cut loose.
Deep into stoppage time Daggers striker Paul Benson almost grabbed a consolation when he out-paced Quinn and rounded Mawson but fired his shot against the outside of the near post.