Grant Holt's early goal was enough to continue the Reds' winning run and pushed them up to 7th in League One.
Joint caretaker manager Barlow told the club website: "To say the game was tense doesn't get anywhere near how we felt, the game was on a knife edge.
"Tranmere tested us to the limit, they put us under a great deal of pressure, but I was pleased with out players' desire, determination and overall resilience."