Former Borussia Dortmund right back Marius Wolf cut inside and curled home with his weaker left foot just after the break for his first Augsburg goal in Sunday's
St Pauli, captained by Socceroos midfielder Irvine, complained about a possible handball and foul in the build-up but the video assistant allowed the goal.
Phillip Tietz then made it 2-0 on 67 minutes when he volleyed in a deep cross from close range before Carlo Boukhalfa cut the deficit with St Pauli's first goal of the league season.
Substitute Yusuf Kabadayi sealed the win on the break in stoppage time.
Hamburg-based St Pauli, seen as a cult club in Germany due to their brown jerseys and left-wing fans, were left reeling in the close season when promotion-winning coach Fabian Hurzeler left for Brighton.
New boss Alexander Blessin, a German who impressed at Belgium's Union Saint-Gilloise last term, took over but his side sit second-bottom.
Augsburg's Danish coach Jess Thorup, who penned a new deal until 2026 on Thursday having easily kept them up last term, secured his first win of the nascent league campaign to move up to 10th on 4 points.
Mainz welcome Werder Bremen in Sunday's later game.
Germany's five Champions League entrants played on Friday or Saturday to give them extra preparation time for the revamped competition starting this Tuesday, Wednesday and Thursday.
Bayern thumped promoted bottom side Holstein Kiel 6-1 away on Saturday, with Harry Kane scoring a fifth Bundesliga hat-trick, as they became the only German top-flight team to take a maximum nine points from three games so far this term.
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