Porter scored one and made the other two in a win that revives Pool's hopes after some disappointing performances lately.
There was a quiet start to the game as the two sides displayed more nerves than ambition and a lot of early passes went astray.
Town should have taken the lead on 22 minutes when Sammy Igoe's run from his own half split the home defence and he set up the unmarked Christian Roberts on the right of the area. But he delayed his shot and home keeper Jim Provett raced off his line to push it wide.
That was Town's one and only first-half effort on target and on 31 minutes Hartlepool took the lead with their own.
Matty Robson's free-kick wide on the left found Adam Boyd and he burst into the area before squaring the ball for strike partner Porter who controlled before chipping over Rhys Evans for his 15th goal of the season.
Seconds before the break, Town defender Sean O'Hanlon broke forward and sent his long-range shot on to the top of the bar and behind.
But they were shaken again three minutes after the break when Porter broke from wide on the right, beating three men on the way, and played the ball into the path of Thomas Butler who slammed in a debut goal from the edge of the area.
Swindon's best player, Igoe, was determined to get his side back into the game but his long-range drive smacked off the face of the bar and their last chance was gone when Provett made a brilliant one-handed save from a curling free-kick by Grant Smith.
Hartlepool sealed victory eight minutes from the end when Porter again broke free and played a perfect short pass into the path of skipper Richie Humphreys who drove in the third from the edge of the area.