Ryan Yates put Forest in front in Friday night's match with a rare goal before Jamie Vardy equalised for the home side. The visitors were much the better side in the second half and Woods' double took them to a comfortable victory.
Leicester goalkeeper Mads Hermansen made a stunning save from point-black range to deny Nicolas Dominguez, Forest winger Callum Hudson-Odoi struck the post and Yates missed a sitter as the visitors should have won by a greater margin.
Forest move to 16 points from nine matches and into the top five, though they have played a game more than the teams around them. Leicester stay in 14th place with nine points from as many fixtures as they continue to leak goals.
Wood's second-half double against his former team marked his sixth and seventh goals in nine games. On each occasion he has scored, Forest have won or drawn.
"It's all down to the team," a modest Wood said. "They supply me with a lot of chances. I'm not one who's going to beat four players and stick one in the top corner. I rely on the service of my teammates and they just keep delivering for me.
"We must keep doing what we are doing all through the season, keep building and getting better."
Forest led on 16 minutes when Leicester twice failed to adequately clear from a corner and Yates drilled the ball into net from 25-yards, the second Premier League goal of his career.
First Facundo Buonanotte tried to dribble out of his own box and was dispossessed, before James Justin's feeble clearance fell invitingly for Forest captain Yates to score.
The lead lasted seven minutes before a flowing Leicester move found Harry Winks wide on the left and his inviting ball across the six-yard box was poked into the net by Vardy.
Dominguez seemed destined to score before he was brilliantly denied by Hermansen, but Wood put the visitors back in front two minutes into the second period, punishing his former side with a shot on the turn from 15 yards.
Forest were inches away from extending their lead as Hudson-Odoi curled the ball onto the post but the visitors would not be denied.
Leicester defender Wout Faes failed to deal with a long ball from Forest goalkeeper Matz Sels and Wood looped a header into the net from 10 yards.
Leicester boss Steve Cooper is still admired at Forest, the club he coached back into the Premier league after a 23-year absence in 2022. But he was scathing of his side's errors on Friday.
"It is self-inficted, it is on all of us and we have to take responsibility for how the game panned out," Leicester manager Steve Cooper said.
"It is a set-back after winning a few games coming into this. We got punished for the poor giveaways that led to their goals."Â
- with The AP
