Hoskins controlled Martin Woods' long pass forward and lashed the ball on the fly past Paul Smith from 12 yards.
That looked to have won the game but Tyson's 88th minute strike salvaged a point for the league leaders when he raced through and fired past Neil Cutler.
Rotherham made a bright start when Ritchie Partridge turned his marker and fired wide.
Despite playing against a strong wind, Rotherham continued to take the game to Forest and came close again on ten minutes when Delroy Facey flicked David Worrell's cross wide.
Forest midfielder Sammy Clingan then brought a superb save from Cutler with a stunning left-foot volley from 20 yards.
The league leaders were growing into the game and on 16 minutes Kris Commons shot wide from the edge of the area.
Rotherham had a shout for a penalty on 21 minutes when Pablo Mills' effort appeared to be handled on the line.
Woods then curled a free-kick wide of the post as half-time approached.
Forest had a great chance to open the scoring on 49 minutes when James Perch fed Commons through the middle but Cutler was out to thwart him with his legs.
Hoskins lit the game up with his wonder goal on 59 minutes, controlling Woods' clearance and firing past Smith.
Rotherham were still threatening and on 68 minutes from a Woods corner, former Forest midfielder Eugen Bopp volleyed wide from 20 yards.
Hoskins almost had a cheeky second when his quickly taken free-kick was pushed away by Smith. Then he was played through by Bopp and again denied by Smith.
Then on 88 minutes Tyson punished Rotherham when he raced on to a long ball and beat Cutler with a shot from 15 yards.