Substitute Paul Edwards won the match for Wrexham with a stunning late goal. He ran onto a cross field pass from Carlos Edwards, beat three tackles as he cut in from the left and hammered his shot past a startled Neil Moss.
Lee Trundle had given Wrexham a flying start with an early goal when Carlos Edwards flicked the ball over from the right and the burly striker was on the edge of the six-yard box to direct a powerful header inside Moss' left post.
Bournemouth switched tactics to ease the pressure with men making deep runs from midfield causing Wrexham plenty of problems.
Dan Bennett cleared off the line from a Steve Fletcher shot as Wade Elliott came sliding in, but on the half hour Thomas levelled the score. He got the final touch in a goalmouth scramble after Paul Whitfield partly blocked James Hayter's shot.
The change of tactics continued to pay dividends for The Cherries when they took the lead through their star man Hayter, whose 30-yard drive flew in off a post. It came after a long ball upfield bounced off Bennett and Steve Fletcher took it on and pulled the ball back for Hayter to take aim.
Wrexham made a double substitution and took a big gamble with the switch to three strikers often leaving them stretched at the back.
Andy Morrell levelled again in the 69th minute with goal again set up by the busy Carlos Edwards.
Cherries boss Sean O'Driscoll said: "We are disappointed. After scoring two goals away from home we should have got something out of it. Wrexham got the points but it could easily have been us." Wrexham manager Denis Smith said: "Their keeper made some unbelievable saves. It's pleasing to win at home because we need to bring more people through the gates. The score could have been anything, even six goals apiece. It was great entertainment."