The Saddlers had pegged the hosts back after Robin Shroot's opener on Tuesday night but Tansey opened his account for his new club in the most spectacular fashion as the Boro claimed a deserved three points - building on three successive home draws and extending their unbeaten league start, which also ended Walsall's five-match unbeaten run.
After an uneventful opening 24 minutes at Broadhall Way, Stevenage went ahead when Shroot controlled David Gray's long pass before firing a fine shot across David Grof and into the bottom corner.
Walsall drew level just before the hour mark when George Bowerman was given the simple task of heading Jamie Paterson's terrific cross into the net from a few yards.
However, Tansey produced something truly special after receiving the ball from Anthony Grant, his 30-yard effort rocketing into the top corner and leaving Grof grasping at thin air.
The hosts made the result safe with four minutes remaining when Tansey's precise cross picked out Lucas Akins at the back post and he volleyed into the ground and into the far corner.