Skipper Michael Nelson put Hartlepool ahead from close range in the 19th minute but veteran striker Nicky Forster levelled before Andrew, on loan from Crystal Palace, headed the winner.
Adams said: "This is a big weight off our shoulders, and I am delighted for the players as we have struggled to perform at home."
Adams has brought in five players during January and hopes to add Oldham forward Craig Davies on Monday in a two-and-half year deal.
But he insisted the influx does not mean highly-rated striker Glenn Murray is on his way out, adding: "I have no intention of selling Glenn. I have had no enquiries."