A stunning goal from Jamie Guy gave Cambridge their first win away since mid-November and only the second of the campaign.
In fact United made a mockery of their record of 11 defeats away from the Abbey Stadium by taking a richly-deserved three points.
Woking looked flat after their emotional FA Trophy quarter final win at Stafford and were unable to raise themselves without four regulars.
Cambridge started well and came close when former Cardinals' mid-fielder Jon Brady swung over a trade mark corner from the left. Centre-back Andy Duncan met it with a looping header which was destined for the net before defender Paul Watson hooked it off the line.
United were buzzing going forward, and on-loan striker Guy came close to scoring when he picked up a Brady pass on half way before embarking on a run down the right. With the Cardinals' defence backing off, he cut inside on to his left foot before unleashing a superb effort which forced Woking's England keeper Shwan Jalal to arch back and tip over his cross bar.
Woking struggled to make chances without top scorer Justin Richards, and Jalal was kept busy, making a superb one-handed save from Fola Onibuje.
Then Guy turned to crack a wonderful shot past Jalal from 25 yards for the winner, and thanks to a brilliant save from Scott Howie, United clung on to the point.
United boss Rob Newman said:" We know we've got it in us to win matches because of our home form, and we have to get this sort of result week in week out to show we are no push-overs away from home."