In a pulsating clash at Deepdale, Slaven Bilic's side dominated the first-half with Matt Phillips and Kyle Bartley both coming close to scoring
The hosts improved significantly after the re-start with Sam Johnstone making a brilliant stop to deny Daniel Johnson.
Alan Browne also saw a fierce drive spectacularly blocked by Nathan Ferguson.
But Albion won it the death when Declan Rudd was judged to have fouled Kyle Edwards in the box.
The decision sparked controversy with the home crowd adamant the winger had dived.
Austin, though, kept his composure to send the keeper the wrong way from the penalty spot and earn his side a fifth straight victory.
Unsurprisingly, Bilic opted to keep faith with the team that was so impressive against Bristol City when naming his starting line-up.
It meant Albion continued in a 4-2-3-1 formation with Hal Robson-Kanu the lone striker, Matheus Pereira in the number 10 role and Grady Diangana and Matt Phillips out wide.
Preston entered the game rocked by injuries with defensive stalwarts Patrick Bauer, Darnell Fisher, Ben Davies and Andrew Hughes all ruled out. Midfielder Paul Gallagher was also absent from the matchday squad.
And that meant Neil had to shuffle is back with the hosts lining up in a 4-5-1 formation with Jayden Stockley up front.
In what proved to be an intriguing opening 20 minutes, it was Albion who dominated the ball with Pereira and Diangana, in particular, linking up well.
But with North End battling admirably, Bilic's side struggled to create clear goal-scoring opportunities.
Eventually, though, their dominance began to tell.
Phillips whipped in a dangerous ball which Robson-Kanu met but was unable to turn towards goal.
Nathan Ferguson then carried the ball 60-yards before seeing a rasping drive from the edge of the box tipped over by Declan Rudd.
The hosts had seemed content simply keeping the Baggies at bay.
But they almost opened the scoring midway through the half when - from a throw-in - Sean Maguire escaped the attentions of Ferguson.
From a tight angle, the midfielder then saw a powerful strike beaten away at his near post by Sam Johnstone.
Albion responded by creating two glorious chances to open the scoring.
First Phillips hit a delicious, curling, effort from the edge of the box which sailed inches wide.
A pinpoint Phillips delivery from a free-kick was then met at the back-post by Kyle Bartley.
But from close range, the defender swept the ball wide when he really should have scored.
Albion's momentum continued for the rest of the half with Bilic's side now in complete control.
Defending deep and in numbers, though, North End were doing just enough to keep them at bay.
Pereira and Semi Ajayi both saw efforts blocked inside the box.
Phillips then forced Rudd into an excellent low save with a fierce low drive from 20-yards.
But despite having enjoyed 67 per cent possession, the Baggies made their way off at the break having failed to find that elusive opening goal.
North End showed a lot more ambition following the re-start with Bilic opting to switch Phillips for Kyle Edwards just past the hour mark.
Suddenly, though, it was Neil's side who were on top with the hosts creating two glorious chances to break the deadlock.
First Sam Johnstone made a fantastic finger-tip save to keep out a
Daniel Johnson effort from 20-yards.
Romaine Sawyers then lost possession in his own box with the ball then worked to Alan Browne eight-yards out.
The midfielder hit a fierce drive which seemed destined to fly into the net.
But Ferguson threw himself in front of the ball to spectacularly keep it out.
With 15 minutes to go, Bilic introduced Charlie Austin with Diangana the man to make way.
It meant Albion continued in their 4-2-3-1 system but with Pereira on the right, Edwards on the left and Robson-Kanu behind Austin.
The changes gave the Baggies added impetus but with both teams struggling to create clear-cut chances it looked as though the game would peter out into a draw.
But in 89th minute Albion won a penalty when Rudd was judged to have brought down Edwards in the box.
Austin stood over the spot-kick and calmly sent the goalkeeper the wrong way to win the game in dramatic fashion - with the result ensuring the Baggies became the first team to win at Deepdale this season.
Albion (4-2-3-1): Johnstone, Ferguson, Bartley, Ajayi, Gibbs, Livermore, Sawyers, Phillips (Edwards 61), Pereira, Diangana (Austin 75), Robson-Kanu (Krovinovic 83).
Subs not used: Bond, Hegazi, Furlong, Barry.
Preston (4-4-2): Preston: Rudd, Pearson, Browne, Johnson, Storey, Rafferty, Stockley, Huntington, Maguire, Barkhuizen, Potts (Harrop 88).
Subs not used: Ripley, Bayliss, Ledson, Armer, Nugent, Bodin.