Barnet made a dream start when highly-rated winger Albert Adomah steamed past George Friend before crossing for Hyde to slam into the net from close range.
The Lions responded well and came close to an equaliser after 17 minutes when Gary Alexander headed David Martin's cross inches over the bar.
Jason Price should have levelled after 25 minutes after Alexander sent him clear but after beating goalkeeper Jake Cole his shot hit the bar.
The South Londoners suffered a big blow 10 minutes before the break when captain Paul Robinson was carried off in his first game of the season.
The loss of the talismanic defender was felt soon after the restart as Adomah flashed a shot just wide of goal before Yakubu doubled the lead after 65 minutes. Clovis Kamdjo headed Adomah's corner into a crowded box and Yakubu headed home to end the Lions resistance.