Harry Kane scored with his first shot at the City Ground
Forest were positive throughout and began on the front foot but Kane punished them with a clinical finish on the break within five minutes.
Goalkeeper Dean Henderson later denied Kane from the spot and made several more important saves.
Kane confirmed victory for Spurs late on, heading in from close range.
Antonio Conte's side were made to work for their victory as Forest, pushed on by a noisy and optimistic home crowd, kept themselves in the game for large periods.
Summer signing Morgan Gibbs-White - on his first start for Forest - and forward Brennan Johnson were particularly lively for the hosts but Tottenham had numerous opportunities to extend their lead.
Son Heung-min came close either side of the break, Kane had efforts well blocked by Forest defender Joe Worrall, and Dejan Kulusevski curled a good strike wide of the post in the second half.
Henderson's save to deny Kane from the spot - after Steve Cook's handball on the line - was quickly followed by a huge chance for Forest's Neco Williams but he could not find the target.
Forest continued to push for an equaliser but Kane dealt the ultimate blow when he headed in substitute Richarlison's cross.
The points deservedly went to Spurs but it was an entertaining fixture with plenty of positives for newly promoted Forest.
Kane's 200th league goal arrived within five minutes to briefly dampen the spirits of a buoyant home crowd, finishing off an excellent, swift counter-attacking move by Spurs.
Tottenham produced several more of those attacking moves as Forest took control of the game in their search for an equaliser but were always vulnerable.
The chances grew for Spurs as Forest attacked more in the second half but Henderson was cheered enthusiastically with each important save to deny Son and Kane.
It was a game of fine margins as Tottenham survived periods of pressure from the hosts, while Forest defended bravely but could not convert their chances.
After Henderson's penalty save, Williams could have made it 1-1 when Forest immediately attacked the other end but his half-volley bounced inches wide of the far post.
Tottenham still could not shake off Forest's attacking threat until Kane scored the decisive second.
-- Courtesy of BBC Sport