Harrogate pressed from the start, George Thompson forcing a save early on from Mark Cousins before he shot across the face of goal and wide, both inside the opening 4 minutes.
Cheye Alexander put a first time volley wide of the left post 10 minutes in. Nana Kyei raced through the defence soon after but delayed his shot too long and eventually his path to goal was blocked.
Shaq Coulthirst had an effort saved by Belshaw, the ball fell to Jack Taylor awkwardly but his header landed on the roof of the net.
Just as the Bees were growing into the match, they were dealt a sucker punch as the hosts took the lead.
After a quick break, the ball fell to Jack Emmett on the edge of the box and he curled it home despite Cousins getting a glove on the ball.
Three minutes later, it was 2. A Joe Leesley corner was hit back across goal by Callum Howe and headed home by the unmarked Liam Kitching.
After the break, Jack Muldoon’s turn and shot went wide. Craig Robson’s header from Taylor’s corner would go over the bar soon after.
Barnet were awarded a penalty in the 51st minute as Coulthirst was fouled. Conversations between Coulthirst and Byron Harrison followed as to who should take, Coulthirst would step up but his low effort was saved by Belshaw.
Ephron Mason-Clark, who was making his first start of the season, cut inside but shot wide of the right post from the edge of the box.
Substitute Josh Walker poked Dan Sweeney’s pass goalbound but his effort was met by Belshaw. Cheye Alexander’s cross was headed wide by Sparkes in the 83rd minute.
Belshaw was called into action again when he had to tip Charlee Adams’ effort around the post in the final chance of the game.
Barnet – Cousins, Alexander, Johnson, Robson (c), Adams, Harrison (Walker, 68), Coulthirst, J. Taylor, Kyei (Sparkes, 64), Sweeney, Mason-Clark
Unused – Matrevics, Fonguck, Tutonda
Attendance -1,381 (Unsegregated so no away figure)
Referee – Simeon Lewis