The Pilgrims were nowhere near their best until a late flurry after they had fallen behind to two goals midway through the second half from Vale striker James Wilson.
They had chances to have got back into the game after that but the finishing touch eluded them as their hopes of a 10th successive home league win were shattered.
Argyle could have no complaints either as despite their improvement late in the match Vale had been the better side overall and posed them plenty of problems throughout.
The Pilgrims did at least retain their position at the top of the table after Ipswich Town conceded an equaliser in the sixth minute of added time as they drew 1-1 at home to Fleetwood Town and stayed a point behind them.
Steven Schumacher made three changes to his starting line-up as Argyle played their first league game in 13 days since the 2-2 draw away to Burton Albion.
James Wilson returned from an ankle injury and slotted into central defence, in between Nigel Lonwijk and Macaulay Gillesphey.
Niall Ennis was included to play in one of the two 'number 10' positions along with Morgan Whittaker, while Ryan Hardie led the Pilgrims' attack.
The trio of Brendan Galloway, Matt Butcher and Sam Cosgrove dropped down to the bench, with the substitutes also including the fitagain Danny Mayor.
Vale were unchanged from their 1-0 home win against Charlton Athletic on November 19 as they lined up in a 3-4-1-2 formation.
Bali Mumba was at right wingback for Argyle and had the first shot of the match in the third minute but his attempt from the edge of the Vale penalty area was easily Steven Sc saved by Jack Stevens.
With Schumacher serving a one-match touchline ban it was assistant manager Mark Hughes who stood in the technical area as the action took place.
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