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Jorge Grant's opener on 61 minutes had the Championship club dreaming of a Capital One Cup upset over their Premier League counterparts.
The game nearly exploded into life after a quiet opening when 20-year-old Ben Osborne rattled the crossbar for Forest following a mazy run.
Spurs responded well to that near miss and went close themselves not long after, with Townsend firing narrowly wide of the post from 25 yards.
Soon came the turn of Federico Fazio to try his luck from range, but the Argentine fired over the bar as the Championship side did enough to earn a half-time draw.
That acted as a wake-up call for Spurs and second-half substitute Mason fired them level in fine fashion on 72 minutes.
With their tails up, the Lilywhites went in search of further reward and nearly found it when Townsend rattled the crossbar with a free kick shortly after.
It proved a sign of things to come, as Townsend's 25-yard hit was deflected past Dorus de Vries by Soldado on 82 minutes, before Kane sealed the win in the dying stages.