North End boss Darren Ferguson saw his men establish a 3-1 lead after 70 minutes of Saturday's Championship derby contest at Turf Moor as Jon Parkin added to earlier goals from Adam Barton and Keith Treacy.
Yet Chris Iwelumo, who opened the scoring, scored twice in the closing stages after Billy Jones' dismissal to complete his hat-trick before homegrown hitman Rodriguez headed home the winner.
Sir Alex Ferguson - whose Manchester United side had been denied victory at Everton earlier in the day in similarly dramatic fashion - was at Turf Moor to see his son's team in action.
United duo Matty James and Josh King are on loan at Preston and both youngsters made the starting line-up.
Preston began in vibrant fashion when King tried his luck from 18 yards but Daniel Fox made a fine block to avert the danger.
Moments later former Blackburn trainee Treacy hit a fierce left-foot shot from 20 yards which drew a smart stop from Clarets goalkeeper Brian Jensen.
But with eight minutes played, Burnley went in front when a superb cross from former Preston winger Ross Wallace reached Iwelumo and he headed home.
In the 14th minute, Wallace went close from 30 yards with a fine effort as Burnley threatened to claim a second.
Yet midway through the first half Preston drew level when rookie midfielder Barton showed impressive pace and strength and fired home a right-footed shot from 12 yards into the bottom corner.
In the 28th minute, King succumbed to injury and was replaced by former Cardiff winger Paul Parry.
Three minutes later, Preston defender Jones hit the crossbar with a 25-yard strike and moments later his side were level.
Treacy showed neat footwork and pace to find space inside the left-hand side of the hosts' penalty box before a superb low shot flew past Jensen and into the bottom corner.
Preston went in search of a third goal after the break when Treacy hit an 18-yard shot which Jensen held comfortably.
The visitors went close again moments later when an inswinging corner from Wallace was met by defender Clarke Carlisle at the far post.
His effort flew just wide but Preston claimed their third with 20 minutes remaining when Parkin connected with a fine left-wing cross from Treacy and volleyed home right-footed from 10 yards.
Yet Preston lost Jones with 12 minutes remaining after he collected his second yellow card and a late rally reaped rich rewards.
Iwelumo produced a fine volley to make it 3-2 and then produced a deft flicked header - after Graham Alexander's cross skimmed off Jack Cork's head - to draw the hosts level.
But there was more drama to come as Rodriguez headed home when unmarked six yards out.