The Lions' seven-game unbeaten grand slam reached a conclusion after Piroe struck in the initial seconds of the final part.
Rout leaves Millwall four focuses untied of the main six with six games remaining.
They will require a solid completion to the season assuming that they are to gotten through the clogged race for a play-off spot.
Swansea, who move to fourteenth, have an excessive amount to do to arrive at the end of the season games, however Russell Martin's side are giving promising indications in front of next season having guaranteed 10 focuses from their last four games.
There had been an inclination that this apparatus would be interesting for the guests on the rear of their important success at Cardiff.
Having accomplished the main association twofold throughout the entire existence of the south Wales derby, Swansea wobbled in the initial minutes when Daniel Ballard headed a Jed Wallace corner over the bar.
However Swansea settled and started to pose inquiries with their brand name passing game, with Michael Obafemi seeing the most obvious opportunity with regards to the main half saved by Bartosz Bialkowski as he met Hannes Wolf's cross with a sliding half-volley.
Jay Fulton's long-officer constrained Bialkowski to repel, and the Millwall goalkeeper was approached again to accumulate Piroe's low shot.Millwall, who yield not many objectives however don't score some either, seldom compromised as the half wore on, despite the fact that Swansea were thankful to see Jed Wallace's shot from the edge of the area divert wide of the post.
The cutting edge showed up when the exquisite Piroe moved the ball wide for Cyrus Christie and afterward progressed into the area.
Murray Wallace hindered Christie's low cross - yet just prevailed with regards to teeing up Piroe to bore home the eighteenth objective of his presentation season in English football at the close to post.
Millwall answered, with George Saville volleying a yard wide before Danny McNamara's low drive was parried by Andy Fisher.
Jed Wallace then, at that point, pulled a shot across the face before Benik Afobe's 90th-minute header cruised over bar, meaning Swansea could praise a third progressive away success.
Millwall chief Gary Rowett:
"I thought first half was challenging as far as we were concerned. Whenever we squeezed, in some cases you need to face that challenge. They play round it very well, they are a decent side under lock and key and they are great at what they do.
"I think they have begun to see somewhat more consistency in their game.
"I almost rolled out the improvements at half-time. I felt a couple of looked a piece leggy after the end of the week which was disheartening. I felt we had somewhat more dash about our play however it's a truly unfortunate objective to surrender soon after half-time.
"For the last half hour it was all us. It was us making the possibilities however we must improve. We were unable to observe that front line at this phase of the period, when you need to track down it."
Swansea lead trainer Russell Martin:
"That was just as great as Saturday in a totally different manner. The enthusiastic energy that was applied on Saturday removed a ton from the folks and they likewise partook in the success, which they ought to have done.
"Now and again there was some lovely football. They were so courageous against an in such great group structure and battling to get to the end of the season games.
"I shared with Gilly (associate Matt Gill) on the sideline, I simply feel so thankful for what they are doing, what they are getting tied up with and how fearless they are being.
"We have at last climbed a smidgen in the table. We are in great structure. We have kept three clean sheets in succession, we are unbeaten in four. We are a lot of a work in progress however the young men are truly developing."
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