Union played out a 1-1 draw in their league opener at Mainz last weekend, but kept all three points in their first home game this term.
The triumph came thanks to Benedict Hollerbach's goal in the 34th minute.
Lucas Tousart had his effort denied by goalkeeper Nikola Vasilj, but in the resulting corner, the ball fell to Hollerbach who fired a powerful first-time effort from the edge of the box into the net.
"We can certainly be more dominant, we can certainly be better. The coach was not happy," Hollerbach admitted after the match when speaking to broadcasters DAZN.
"It wasn't a good game. The important thing is the result, but we can do better," he said.
Union played without Robin Gosens and managing director Horst Heldt confirmed the midfielder will leave the club.
He didn't give details on Gosen's future, but according to media reports he will join Fiorentina in Italy's Serie A.
"Until 10 past four, I assumed that Robin would be on the pitch and playing today. Then the news came and we realised that (he was leaving)," Heldt said ahead of the match.
St Pauli suffered a second consecutive defeat after losing 2-0 at home to Heidenheim in their first Bundesliga match since 2011 last weekend.
"In the second half we pressured, had ball possession, but didn't create real big chances, I think that lacked. We have to be more effective," striker Johannes Eggestein said.
Coach Alexander Blessin said he didn't see "any clear chance" for his team.
Champions Bayer Leverkusen have a top clash against RB Leipzig on Saturday, while Bayern Munich host Freiburg on Sunday.
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