George Baldock scored the clincher as Tamworth ended Woking's four-match unbeaten run.
Tommy Wright gave the visitors the lead from close range and Adrian Cunnington made it 2-0 with a powerful shot that beat Woking keeper Aaron Howe.
Kevin Betsy pounced on a rebound from Gavin McCallum's shot to pull a goal back for the home side.
Baldock restored Tamworth's two-goal cushion before Mike Cestor grabbed a late consolation for the Cardinals.
VIEWS FROM THE DRESSING ROOM
Woking manager Garry Hill told BBC Surrey:
"I am starting to see some jadiness in some of the players and people appreciate we are part-time. It is a full-time league and we've seen over the last game that we look tired.
"We found ourselves 2-0 down at half-time and with a mountain to climb and we didn't get going and whoever you play against you can't turn round and not start well and get a result.
"Whoever we play against it always going to be tough and we gave ourselves too much to do."