Connor Jennings slotted Wrexham ahead with an early penalty after Scott Doe brought Kayden Jackson down in the box.
Jackson almost added to the hosts' lead but hit the side netting after rounding Boreham Wood keeper James Russell.
Defeat leaves Boreham Wood just one point above of the relegation zone in 19th.
Gary Mills' Wrexham picked up a fifth consecutive clean sheet and are unbeaten in their last eight league games.
Wrexham boosted their National League play-off hopes with a fourth win in five games while adding to Boreham Wood's relegation worries.