After a first half which saw plenty of chances created but none taken, all three Boro goals came after the break with Dipo Akinyemi, Robbie Sweeney and sub Adam Marriott finding the back of the net.
Teddy Sheringham's team selection saw Dean Wells, Jamie McCombe, Brett Williams, Rohdell Gordon and Dipo Akinyemi all start alongside a number of scholars and Williams saw an early effort smack against the crossbar after just three minutes.
Playing in front of a club record crowd of 381, the Citizens were particularly lively in the first half and Stevenage goalkeeper Billy Collins, on work experience from Reading had to be alert to make a couple of top saves.
His opposite number was also in good form, twice denying midfielder Liam Brady and then saving from both Akinyemi (twice) and Williams as the half progressed.
Akinyemi broke the deadlock seven minutes into the second half, smashing home from close range after a ball in from Williams.
With 25 minutes remaining Adam Marriott was introduced into the action - a welcome sight for Boro fans after his long-term knee injury.
Five minutes later Collins made a fine save at one end before Stevenage countered and doubled their advantage. Akinyemi led the break, drawing defenders towards him, before finding Robbie Sweeney who cut inside and found the far corner.
Marriott capped a lively sub appearance with a late third, firing home a free-kick from just outside the area.
The 3-0 win marked a good evening's work for Stevenage, with several first team players getting minutes and a number of Under-18s impressing. With Cheshunt beating Royston in their first round fixture a trip to Theobalds Lane beckons in round 2. Details of that fixture will be announced when confirmed.
Stevenage: Collins, Slater, Wells (Smyth 46), McCombe, Kerr, Gordon (Marriott 65), Guerfi (McKee 75), Brady, Sweeney, Akinyemi, Williams
Subs not used: Gibson, Croud,