Adam Le Fondre's spot-kick had cancelled out Danny Glover's opener and looked to have given Rochdale a point.
Dale striker Lee McEvilly, who was handed a start after netting twice on Boxing Day, almost grabbed the opener inside four minutes but shot narrowly wide of goal. Moments later his strike partner Chris Dagnall tested Joe Anyon with a header after a teasing cross from Tom Kennedy.
Kyle Perry was unlucky not to grab his first Vale goal when clean through but watched as his shot rolled agonisingly wide. It was a rare chance for Vale who were playing second fiddle to a team pushing for promotion. And it was Perry who went closest five minutes before the interval with Sam Russell needing to tip the striker's header over the bar.
The second half started even with both teams struggling to create any real gilt-edged chances. As the half wore on Vale looked most likely to open the scoring with Perry giving the Dale centre backs a torrid time in the air. However, the former Chasetown striker was replaced by Thompson in the 68th minute much to the bemusement of the home contingent.
It was little surprise when Vale took the lead in the 74th minute as Glover prodded in Anthony Griffith's cross for his first goal of the season.
The visitors pressed forward for the equaliser and it came from the spot after Le Fondre was bundled over by Luke Prosser in the area eight minutes from time. The substitute dusted himself down and sent the ball high into the net past the helpless Anyon.
But it was another substitute Thompson who struck the decisive blow in stoppage time to give Vale the points.