Wood, who had a goal disallowed in the first half for offside, opened the scoring in the 56th minute when he got away from Michael Mancienne to net his sixth goal in his last four league games.
The hosts doubled the lead with 16 minutes remaining when Souleymane Doukara cracked a thunderous strike into the net from the edge of the area.
Leeds moved third in the second tier on 51 points, nine adrift of leaders Brighton & Hove Albion, while Forest are 19th, five points clear of the relegation zone.
(Reporting by Toby Davis; editing by Ed Osmond)
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