The striker's 67th-minute goal, bundled home after his initial shot had been blocked on the line, was enough to earn Colin Calderwood's side a 1-0 win over hard-working Luton Town.
With Carlisle and Doncaster both dropping points, Forest still have a glimmer of hope of claiming automatic promotion.
But, as they extended their unbeaten run to five matches, they are in good form going into the play-offs.
The game did not spring into life until the 11th minute, when Tyson's shot was blocked at the near post, leaving Keith Keane to make a vital block to deny Kris Commons the chance to slot home the rebound.
A surging run from the back saw Wes Morgan carry the ball into the opposition half and kick-start a flowing move that culminated in a bending 20-yard shot from Commons, which Dean Brill saved in acrobatic fashion, palming around the post for a corner.
Sammy Clingan's delivery from the flag kick picked out Ian Breckin at the near post, but the defender's flicked shot was cleared off the line by Sol Davis, just as it threatened to bounce inside the far post.
Commons forced another smart save from Brill with a crisp low drive, while Chris Cohen sent a dipping volley narrowly wide of the post.
But, despite winning a succession of corners before the interval, Forest were unable to make the breakthrough against a resolute Luton side, with Tyson's control letting him down as the ball bounced loose in the box.
Although, while they had defended well, the best the visitors could offer was a deflected shot from Sam Parkin that left Paul Smith with a simple save.
Forest brought on Garath McCleary after the break and the substitute had an immediate impact, setting up James Perch for him to shoot over from the edge of the box and, two minutes later, crossing to the far post where Julian Bennett just failed to connect.
But Luton also came close to breaking the deadlock as Parkin thumped a header against the bar and Stephen O'Leary saw a low drive blocked by Breckin, following a moment of panic in the Forest defence.
Forest finally took the lead after some great work from Commons down the left. He left two defenders in his wake before crossing to the far post where McCleary headed back across goal.
Tyson initially saw his low shot blocked on the line but Luton could do little as the striker lashed home the rebound.
Clingan could have made it 2-0 with a stinging volley that dipped just wide. But Luton also came close as Matt Spring forced a fine save from Smith with a powerful drive, while Parkin was terribly off-target with a golden opportunity in the 82nd minute.
Tyson was denied a second goal for Forest as Brill made a fine save in stoppage-time.