The former Wycombe striker was sent off in Forest's 2-1 defeat at Brighton last season for elbowing Adam El-Abd.
He made amends with clinical finishes in both halves at the Withdean Stadium to take his tally to six goals in the last seven games.
Tyson volleyed the visitors ahead from close range on the half-hour after Grant Holt headed on a Lewis McGugan cross.
Brighton's hopes of mounting a second-half comeback folded when Tyson struck again four minutes into the restart.
Kelvin Wilson's long clearance out of defence should have been dealt with by Joel Lynch but Tyson dispossessed the young centre-half and glided past El-Abd before firing past Michels Kuipers.
Forest were reduced to ten men four minutes later when midfielder Sammy Clingan received a straight red card for a foul on winger Jake Robinson.
The home side, fatigued after trips to Torquay and Doncaster, were unable to take advantage as they suffered their first defeat in 11 matches.
The closest they came to scoring was shortly after Tyson's opener when a snapshot from Dean Hammond was parried by keeper Paul Smith and Nicky Forster drove against the post.
Forest chief Colin Calderwood was delighted by his side's response to their 1-0 defeat at Walsall.
He said: "We were magnificent with ten men, very solid and we were deserved winners.
"The decision to send Sammy off was pretty harsh. It was a booking that's all.
"He did not go in two-footed or over the top, he went in for a hard tackle and was slightly late."
Brighton manager Dean Wilkins added: "It was probably a game too far for us this week.
"It was still a decent performance and in the first half I thought we had the better of it."