The visitors went behind early when goalkeeper Tom King fumbled Andy Haworth's corner and presented Jason Walker with a close-range gift.
Andy Cook doubled the advantage with his 20th goal of the season as he latched on to Jordan Williams' assist.
Barrow have now gone nine games unbeaten while defeat leaves Braintree are one point off the top five.
Barrow registered a fourth successive win as they dented Braintree's National League play-off hopes.