Rickie Lambert smashed in a penalty - which saw Pools skipper Sam Collins dismissed - before teeing-up centre-back Jose Fonte to head in the second eight minutes from time.
Second-placed Saints are ahead of Huddersfield on goal difference with a game in hand, and Adkins believes his side's defence are sending them to promotion.
He said: "Credit to Hartlepool. They were well organised as you would expect and we had to be patient to break them down but got there in the end.
"I want the players to feel 10 feet tall and go out and express themselves and they have gone out and scored two very good goals and earned an important victory.
"We are taking care of business now and we just have to make sure we get our players ready for another testing weekend."
Source: PA
Source: PA