Indeed the final score did not do justice to a York side who went on to completely dominate the second period and who should have wrapped this game up much earlier.
After their opening day defeat Stevenage were looking to make a bright start in front of their home crowd but it was York who began in an aggressive manner.
Indeed Clayton Donaldson took just 22 seconds to get a sight of the Boro goal as he ghosted in at the far post and just touched an effort wide of Danny Potter, making his home league debut in goal for Stevenage.
York looked full of early promise and on four minutes it was the turn of Mark Convery to worry Potter as his first shot was blocked by the defence, while his second effort was blocked with a diving save to his right by the homer keeper.
York looked set to break the deadlock and they found the back of the net just two minutes later when shaky defending from Luke Oliver and Barry Fuller allowed Donaldson to force his way clear on goal and fire a rasping drive high into the roof of the net from close range.
Shell-shocked by the early strike, Boro looked for a tentative way back into the game but their only effort on goal came when Adam Miller lofted a speculative 35-yard effort which easily cleared the crossbar.
New signing Craig Dobson began to warm up the home crowd with some neat runs down the right and with Nathan Peat already on a booking after a foul on Jon Nurse on 10 minutes, Dobson applied too much pressure when he skipped past the York defender on 21 minutes and drew a clumsy foul inside the penalty area.
Adam Miller stepped up to crash the resulting spot-kick high into the net off the crossbar and although the effort was disallowed for encroachment, Miller stepped forward again and drove Boro level with a strike which nestled inside keeper Tom Evans' right-hand post.
After conceding the foul for the penalty and being considered lucky to still be on the field, Peat was substituted by Anthony Lloyd, but it was a change which did not shore up the visitors defence.
George Boyd warmed up to his task as he beat two defenders before drilling a 25-yard effort just wide of the post, while Dobson continued to cause panic as he cut inside on 37 minutes and saw a strike saved with ease by Evans in then York goal.
For their part York also had chances to go in ahead before the break, Craig Farrell had the best of the efforts five minutes before the break when he raced through on a Convery pass.
Although his first effort was blocked by Potter and cleared by Oliver, Farrell was on hand to drive the rebound goalwards. This time however Potter was able to hold on to the ball.
The second half saw a complete change in fortunes of the game as York inexplicably took a stranglehold on the match. From the outset Stevenage were unable to deal with the threat posed and a strike on 49 minutes from Neal Bishop which came back off Potter's right-hand post was a taste of things to come.
Farrell continued to cause the shaky home defence problems with his tireless running and it looked as if he had scored on 56 minutes when he carved out room on the left flank and fired an effort across goal.
Just a minute later Farrell and Bishop teamed up for a neat move which was thwarted at the cost of a corner by Santos Gaia and York almost went back ahead from the resulting-kick when Steve Bowey's ball in was pushed around the post by Potter.
Boro suffered a body blow on 61 minutes when Gaia hobbled off after a challenge and it didn't take long for the visitors to take full advantage. Bowey was the man who made the most of his opportunity as he ran at the static home defence, before curling in a sweet right-footed drive from the edge of the box on 64 minutes.
Bowey came close with another effort just two minutes later as Boro were left on the ropes. York pressed forward with urgency and they made the makeshift Boro defence with Ronnie Henry and Oliver at its heart look distinctly unsteady.
Boro's best effort of the half came out of the blue on 69 minutes when Oliver rose first to meet a free-kick and guided a looping header onto the top of the bar. Nurse followed up the loose ball but his tame effort was driven at the keeper.
Boro boss Mark Stimson made a late switch bringing off the ineffective Tony Thorpe for Chris Sullivan, but despite a last-gasp penalty appeal and Nurse header onto the top of the netting, Stevenage never looked likely to find their way back into the game and have now failed to take any points from their opening two games, while York have an impressive four from two tough encounters.