Captain Jennings gave Wrexham the lead against the run of play with a looping header from Blaine Hudson's cross.
Dominic Vose had two chances to extend the lead while Joe Devera hit the post on his Boreham Wood debut.
James Russell kept the home side in the game, making crucial saves to deny Dominic Vose and substitute Mark Carrington.
The victory sees Gary Mills's side move up to third in the table and five points behind leaders Forest Green, who lost 4-1 at Macclesfield.
Wrexham manager Gary Mills told BBC Radio Wales: "I love the one nils, especially away from home. It should have been four or five. It could have come back to bite us.
"It's the league we're in - it's difficult. We lost on Tuesday and we've gone again here and picked up a result. It's important when you lose to bounce back.
"It's not easy when you have a disappointment like the other night because we shouldn't have lost the game and we've come here and put it right."
Match ends, Boreham Wood 0, Wrexham 1.
Second Half ends, Boreham Wood 0, Wrexham 1.
Foul by Matt Whichelow (Boreham Wood).
Blaine Hudson (Wrexham) wins a free kick.
Corner,  Boreham Wood.
Attempt missed. Rob Evans (Wrexham) right footed shot from outside the box misses to the right.
Substitution, Boreham Wood. Matt Whichelow replaces Charlie MacDonald.
Attempt missed. Adriano Moke (Wrexham) left footed shot from outside the box misses to the left.
Corner,  Boreham Wood.
Corner,  Wrexham.
Attempt saved. Mark Carrington (Wrexham) header from the centre of the box is saved.
Substitution, Wrexham. Lee Fowler replaces Dominic Vose.
Attempt missed. Luke Howell (Boreham Wood) header from the centre of the box is too high.
Corner,  Boreham Wood.
Foul by Jamal Fyfield (Wrexham).
Charlie MacDonald (Boreham Wood) wins a free kick.
Foul by Connor Jennings (Wrexham).
Conor Clifford (Boreham Wood) wins a free kick.
Attempt missed. Dominic Vose (Wrexham) right footed shot from the right side of the box misses to the right.
Corner,  Wrexham.
Offside, Wrexham. Kayden Jackson tries a through ball, but Kayden Jackson is caught offside.
Foul by Charlie MacDonald (Boreham Wood).
Jamal Fyfield (Wrexham) wins a free kick.
Substitution, Boreham Wood. Junior Morias replaces Sam Cox.
Substitution, Wrexham. Mark Carrington replaces James Gray.
Corner,  Wrexham.
Attempt saved. Sean Newton (Wrexham) left footed shot from the left side of the box is saved.
Substitution, Wrexham. Kayden Jackson replaces Wes York.
Attempt saved. Dominic Vose (Wrexham) right footed shot from outside the box is saved.
Foul by Billy Clifford (Boreham Wood).
Dominic Vose (Wrexham) wins a free kick.
Attempt missed. Conor Clifford (Boreham Wood) right footed shot from outside the box misses to the left.
Connor Jennings (Wrexham) is shown the yellow card for a bad foul.
Foul by Connor Jennings (Wrexham).
Luke Howell (Boreham Wood) wins a free kick.
Sam Cox (Boreham Wood) is shown the yellow card for a bad foul.
Foul by Sam Cox (Boreham Wood).
Dominic Vose (Wrexham) wins a free kick.
Substitution, Boreham Wood. Billy Clifford replaces Josh Hill.
Second Half begins Boreham Wood 0, Wrexham 1.
Connor Jennings scored the only goal of the game as Wrexham beat Boreham Wood in the National League.