The visitors named a number of players that won the Premier League 2 Division 2 title last season whereas Barnet made two changes from their midweek victory over Swansea.
Barnet, in their new away kit of all blue, had the first chance of the game, Akpa Akpro delivering a dangerous cross which found John Akinde, but his header was blocked.
West Ham then had a couple of chances in quick succession, with Powell and Diangana both having efforts blocked.
Jack Taylor received the ball in space on the edge of the box following a pass from Shomotun, but his attempt went narrowly over the bar.
20 minutes in, Jack Taylor was taken off as a precaution, Wesley Fonguck replacing him.
Shomotun had two attempts in quick succession. First he saw his attempt from 18 yards go agonisingly over the bar and then minutes later he scuffed a shot wide following good build up play from Akinde.
In the 39th minute, the Bees took the lead. Akinde delivered a great through ball to Jean-Louis Akpa Akpro who then dinked it over the onrushing Matrevics and into the net.
Early in the second half, Fonguck fired a shot at goal which was destined for the top corner, only to be denied by a top drawer save from Matrevics.
On the hour mark, just as Rossi was preparing to fully rotate the side, Barnet doubled their advantage. Shomotun laid the ball off to the overlapping John Akinde who fired it high into the roof of the net.
As part of the 10-man substitution, new signing Richard Brindley game on and almost made in instant impact.
After a good run he fired at goal only to see his effort go just wide of the left hand post.
West Ham pulled a goal back on 72 minutes, Dan Kemp played through Reece Hannam who slotted past Craig Ross.
As the game drew to a close, chances were few and far between. Akinola had a chance with a minute to go, but his low shot was saved by Matrevics.
Barnet will now prepare for Championship side Millwall in their next pre-season friendly next Saturday.
Barnet line-up: Jamie Stephens, Elliott Johnson, Charlie Clough, Ricardo Almeida Santos, Curtis Weston, John Akinde, Jamal Campbell-Ryce (Capt), Jack Taylor, Harry Taylor, Fumnaya Shomotun, Jean-Louis Akpa Akpro
Barnet substitutes: Craig Ross, Richard Brindley, David Tutonda, Simeon Akinola, Nana Kyei, Westley Fonguck, Alex Nicholls, Dan Sweeney, Darnell Smith, Justin Amaluzor, Joe Payne
West Ham United line-up: Rihards Matrevics, Alex Pike (Capt), Vashon Neufville, Conor Coventry, Tunji Akinola, Ajibola Alese, Dan Kemp, Joe Powell, Julian Kristofferson, Grady Diangana, Jaanai Gordon
West Ham United substitutes: Jahmal Hector-Ingram, Tyler Forde (GK), Korrey Henry, Kristjian Belic, Anthony Scully, Reece Hannam, Ben Wells, Oriol Rey, Jeremy Ngakia