Hungary international striker Istvan Ferenczi came back from a five-match injury absence to give Barnsley a first-half lead but Muller pulled off a hat-trick of super saves to deny Preston.
And he then crowned a five-star performance with a fantastic save to turn over a last-gasp spot-kick from substitute Neil Mellor.
The home side's first chance came after 11 minutes when former Preston and Manchester City striker Jon Macken was involved in a slick move that carved open the Preston defence.
Brian Howard burst forward and Macken challenged but the ball fell to Ferenczi who snapped off a shot that needed a super save from Andy Lonergan to keep the match goalless.
Four minutes later Macken was denied by another last-ditch stop from Preston defender John Halls who was making his debut after arriving on loan from Reading.
A Jamal Campbell-Ryce cross was then won by Ferenczi who tossed in a high ball that Macken won in an aerial challenge, and when it dropped Macken's shot was cleared by Hall.
Preston, whose earlier pressure earned them a string of corners, saw an early opportunity denied when Karl Hawley pounced on a ball that had only been half-cleared by the home defence and hit a blistering 22-yard shot that Muller forced over with a strong two-handed save.
But three minutes before half-time, Barnsley made the breakthrough with Ferenczi's third goal of the season.
Howard won a free-kick on the right and whipped it into the near post with wicked accuracy and Ferenczi met it with a glancing header - a super finish.
Barnsley's lead hung by a thread as Preston came back after the break and only two super second-half saves preserved their advantage.
Two minutes after the restart Preston's star performer Darren Carter made a strong run down the left, cut inside and drilled a low shot but Muller somehow dropped to block the chance.
And when Carter produced an inch-perfect header from Paul McKenna's neat chip, Muller pulled of an acrobatic save to push the ball round the post.
Rob Kozluk then pulled back Sean St Ledger in injury time, and although Mellor blasted his spot-kick, Muller made an incredible save.