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."
Woking 01 Howe 02 Newton 05 McNerney 06 Doyle (Williams - 78' Booked ) 08 Parkinson 16 Johnson Booked 04 Ricketts 11 Betsy Booked 12 Davies (Pires - 56' ) 19 McCallum 09 Bubb (Mike - 78' ) Substitutes 18 Beasant 03 Mike 17 Sinclair 07 Pires 14 Williams Tamworth 13 Breedon 06 Marshall 15 Courtney 33 Dempster 35 Taylor Booked 04 Baldock Booked 11 Kerry 18 Till (Gudger - 80' ) 19 Barrow (Kelly - 75' ) 07 Cunnington (Collins - 89' ) 09 Wright Substitutes 31 Belford 17 Gudger 30 Oji 03 Kelly 28 Collins