Wanderers faced a long journey home to figure out how they left Home Park pointless from a first away defeat since the end of February.
The Whites dominated for much of the 90 minutes against a Plymouth side which had started their home campaign with back-to-back League One wins.
But a lack of ruthlessness in both boxes proved costly as Argyle were allowed a soft lead they were then able to defend as the Whites again came up short in front of goal.
There were decent openings for Ian Evatt’s men before falling behind 25 minutes in.
And there were certainly second-half chances to grab at least a point but with the goals not yet flowing - and Argyle keeper Michael Cooper making one incredible save - Plymouth survived and secured victory on the break two minutes from the end of another frustrating afternoon.
Wanderers made five changes to the side that had started against Villa in mid-week and began with the same kind of intensity that had briefly rocked the Premier League side.
Dion Charles, who had put the Whites in front in the Carabao Cup tie, persistently stretched Argyle’s back line as the Whites’ pressing game didn’t allow the hosts to settle.
Conor Bradley forced Cooper to turn an angled shot wide as the teenager ran in behind the Plymouth defence.
And Kieran Lee, starting again after his outstanding performance against Villa, thought he had put Wanderers ahead with 20 minutes gone.
A superb move from back to front involving George Johnston, Kyle Dempsey and Jack Iredale and Charles ended with Charles picking out Lee for a shot that appeared goalbound until striking Plymouth midfielder Bali Mumba inside the six-yard box.
Argyle also saw an effort from Finn Azaz blocked in front of goal following a corner and James Trafford had to save from Danny Mayor.
But when Plymouth did go in front 10 minutes before the break it was against the run of play and a tough one to take for Wanderers.
A free-kick played into the inside right channel shouldn’t have caused too many problems but the dangerous Ennis managed to wriggle free from Ricardo Almeida Santos and knock the ball wide of James Trafford before slotting home.
Wanderers went close to equalising just before half-time when Gethin Jones superbly picked out Iredale whose touch and curling shot would have made it a special goal had the ball gone just the other side of the far post.
But despite dominating possession, Wanderers were struggling to make a clear-cut chance to get themselves back on level terms and with an hour gone Plymouth could have doubled their lead when Brendan Galloway connected with a Matt Butcher corner but from in front of goal steered the ball wide.
With 25 minutes to go, Bakayoko was sent on to try and add more potency and immediately he was involved with a flick round the corner for Charles, who ran out of room to squeeze a shot past Cooper.
Dapo Afolayan and Kieran Sadlier were also added to the mix from the bench and with Wanderers continuing to press they thought they had finally found a deserved equaliser with 10 minutes to go.
Again Bradley provided the outlet down the right-hand side and from his excellent cross, Bakayko powered an effort goalwards on the volley which Cooper remarkably touched onto a post with Galloway clearing as Bakayoko tried to convert the follow-up.
It was all Wanderers as they desperately tried to conjure up an equaliser.
But the Whites have now drawn a blank in three of their last four league games and instead it was Argyle who struck next to secure the points with a couple of minutes to go.
Inevitably the Whites were committed to attack and when Plymouth broke, Ryan Hardie was the beneficiary as he was released by fellow substitute Morgan Whittaker to drive the ball past Trafford with a clinical finish to kill of hopes of a figthtback and confirm the end of Wanderers’ unbeaten away start.
Wanderers: Trafford; Jones, Santos, Johnston; Bradley, Morley, Dempsey (Afolayan 75), Iredale (Sadlier 75); Lee; Kachunga (Bakayoko 67), Charles. Substitutes: John, Williams, Aimson, Thomason.
Plymouth Argyle: Cooper; Lonwijk, Scarr, Galloway (Wilson 85); Edwards, Houghton (Randell 57) Butcher, Mumba (Gillesphey, 85); Azaz (Whittaker, 57), Mayor; Ennis (Hardie 70). Substitutes: Burton, Wilson, Jephcott.
Booked: Ennis, Edwards
Referee: Will Finne