Second half goals from Declan O'Brien and Ryan Guy boosted St Patrick's hopes of avoiding the relegation play-offs in an eventful basement battle at United Park.
The Inchicore men looked destined for a nervous final-day showdown with Shamrock Rovers when they fell behind to an early James Chambers strike.
But they turned it round in a five-minute spell just after the restart, and Chambers went from hero to villain when he was sent off for a challenge on Ryan Guy right on the final whistle.
Alan Mathews' men are safe from automatic relegation following Bray Wanderers' defeat, but their play-off hopes will be badly dented if Chambers is given an additional suspension for his straight red card.
Drogheda, without the injured Jamie Duffy in attack, lined out with only one recognised striker but still took the lead from their first attack in the sixth minute.
The two McGills worked the ball down the right flank, and Brendan's cross was fired home with ease by James Chambers.
Drogheda could have had a second goal as early as the 12th minute when Chambers turned provider with a corner kick that Brian King nodded just wide, and then a Brendan McGill header failed to seriously test Brendan Clarke in the Pat's goal.
Pat's were subdued all over the field, with strikers Declan O'Brien and Mark Quigley having no input whatsoever.
However, former Drogheda star O'Brien almost got a decisive touch to a clever Bobby Ryan chip in the 26th minute, and another familiar face could have struck against his old club on three occasions in quick succession.
Stuart Byrne was defeated by a narrow angle on the first occasion, but on 42 minutes he pounced on a Quigley knock-down to shoot firmly at the target, only for Paul Skinner to produce a fine reaction save.
And on the stroke of half-time an in-swinging cross by Enda Stevens was glanced narrowly wide by the veteran midfielder.
But a fired-up Pat's struck the woodwork twice in the space of a minute on the restart as Skinner brilliantly pushed Quigley's shot onto the upright and Jason Gavin went close from the resulting corner.
Then two goals in the space of five minutes turned the game on its head.
First, O'Brien got on the end of Gareth O'Connor's cross to nod past Skinner, and then the scorer turned provider with a brilliant pass for Ryan Guy who rifled into the Drogheda net from 10 yards.
The shell-shocked Drogs had no response other than an ambitious 40-yard free from Chambers which flew a yard wide of the target, and O'Brien nearly increased Pats' lead on 72 minutes with a header that bounced off the inside of the post before being booted clear.
Ryan could have killed the game off a minute later, but he hooked the ball over the Drogheda crossbar from close range.