Hartlepool's neat attacking football caused major problems for Wrexham, and midfield man Darrell Clarke was the main tormentor as Neale Copper's side collected three points.
Clarke scored twice from close-range in 13 first-half minutes to give the home team a lead they fully deserved.
After 23 minutes it was top scorer Paul Robinson who undid the square Wrexham defence, his throughball giving Clarke the chance to side-step a challenge and slide his low shot in from ten yards.
Then 13 minutes later he was at it again, running from deep to get on the end of a chip into the box from Mark Tinkler, sending visiting keeper Andy Dibble the wrong way before tapping into an empty net from close-range.
Wrexham did have chances on the break, with Carlos Edwards their best hope. But twice good runs by him were wasted by off-target finishing from Chris Llewellyn.
Home keeper Jim Provett saved well between Clarke's two goals from a 30-yard free-kick that Stephen Thomas curled round the wall.
In the second half Provett made good saves on the only two occasions the Pools defence was breached.
First he tipped an overhead shot from Lee Jones against the bar and behind when a goal looked certain, then he dived to his left to pull down a long-range shot from Paul Edwards.
The home team had won the game in the first half with a great attacking display, and then proved they can defend as well in the second when Wrexham staged a spirited rally.
Delighted Pools boss Cooper said: "We won the game in the first half and then won it again in the second when we had to defend as Wrexham hit us back.
"But another clean sheet always pleases me, almost as much as a win. The boys did well and they deserve a lot of praise for the way they've started the season." Wrexham chief Denis Smith was unhappy with the way the goals were given away.
"They were both sloppy and that's not the way we usually play," he moaned.
"In the second half we came back and I felt we did enough not only to get a point, but to win the game. But the ball wouldn't go for us and that's football.
"The performance over the 90 minutes, apart from those soft goals, was a good one. It's a pity about the result."