The home side dominated the early exchanges but were unable to find a way past the impressive James Dormand in the Tamworth goal.
Darryn Stamp twice came close while Jason Goodliffe, Jon Nurse and George Boyd were all within a whisker of putting Stevenage ahead.
For their part Tamworth had just one effort on goal when Matt Redmile saw a flicked header saved by Alan Julian.
Stevenage finally took a deserved lead just four minutes before the break and it was man of the match Boyd who spectacularly fired in from a tight angle after a cross from the left by Anthony Elding.
The home side continued to dominate after the break and doubled their lead when Boyd split the Tamworth defence and passed to Elding to slide the ball home.
Tamworth did threaten a revival when Redmile guided a header home from a free-kick with 15 minutes remaining.
But the rally was shortly lived and Stevenage restored their two-goal advantage when Jason Goodliffe headed in on 79 minutes to confirm the hosts' dominance.
The home side could have added to their total in an impressive final spell which culminated with Robert Quinn guiding a header from the edge of the box onto the top of the crossbar.