The striker slotted home after Sebastian Schachten had robbed Filip Twardzik of possession just before half-time to give the Bundesliga 2 side victory.
A young Celtic outfit ought to have salvaged a draw, but Bahrudin Atajic put a penalty over the crossbar three minutes from time after Paul McMullan had been upended by Tom Trybull.
Celtic boss Ronny Deila gave former Scotland goalkeeper Craig Gordon a start in an otherwise inexperienced side, as his first-team regulars were given a rest ahead of Wednesday's UEFA Champions League third qualifying round clash against Legia Warsaw.
Atajic had an opportunity to open the scoring just two minutes in, but Philipp Tschauner thwarted the young Swedish striker and the goalkeeper had to be alert once again to come off his line and deny Amido Balde when the Portuguese raced clear 11 minutes in.
It was the home side who took the lead five minutes before half-time, though, when Twardzik dallied on the ball and Schachten nipped in to dispossess the left-back and cut the ball back into the path of the onrushing Nothe, who finished with his right foot from six yards out.
Nothe could have doubled his side's lead just after the hour mark, but he fired over the crossbar and Tony Watt spurned a chance to equalise after Eoghan O'Connell picked the striker out but he headed wide.
Celtic goalkeeper Lukasz Zaluska, who replaced Gordon at half-time, tipped over Sebastian Maier's free-kick as St Pauli went in search of a second goal and there was a dramatic finale as Celtic were awarded a penalty with only three minutes remaining.
McMullan raced into the penalty area and was brought down by Trybull, but Atajic put his spot-kick over the crossbar after looking unconvincing in his run-up and Watt flashed a shot wide of the far post as Celtic were consigned to defeat.
